14  BAROMETRIC   HYPSOMETRY. 

The  pressure  term  and  the  temperature  term,  therefore,  are  the  only  ones 
remaining,  subject  to  any  essential  modification;  and  in  what  follows  it 
will  be  seen  how  varied  in  character  the  modifications  proposed  have  been. 

It  is  necessary  to  observe,*  "however,  that  many  of  the  changes  which 
the  formula  has  undergone,  though  of  great  importance  in  themselves, 
were  really  less  radical  than  would  appear  at  first  sight.  As  first  pub- 
lished the  formula  was  ill-adapted  for  purposes  of  calculation.  The  oper- 
ations required  were  complex,  and  the  work  was  tedious.  Transformations 
were  therefore  made  with  the  view  of  reducing  the  amount  of  numerical 
computation,  or  of  securing  a  tolerable  approximation  with  very  little 
labor,  or  of  adapting  the  formula  to  different  standards  of  measure,  but 
not  necessarily  connected  with  the  idea  of  remedying  any  of  its  deficien- 
cies or  increasing  its  theoretical  or  practical  accuracy.  Hypsometrical 
tables  of  greater  or  less  extent,  some  requiring  and  some  avoiding  the 
use  of  logarithms,  and  giving  results  in  English,  French,  or  other  units 
of  measure,  have  been  published  from  time  to  time,  but  in  almost  all 
cases  the  criterion,  according  to  which  the  ultimate  value  of  the  table 
was  to  be  judged,  was  the  more  or  less  close  agreement  of  the  results 
with  those  which  would  have  been  obtained  if  the  formula  of  Laplace 
had  been  applied  rigorously.  The  special  formula  upon  which  each  set 
of  tables  was  based  might  differ  widely  in  form,  though  not  in  substance, 
from  that  of  Laplace.  The  tables  proposed  by  Dr.  Benzenberg,*  by  aid 
of  which  an  observer  performing  a  few  simple  additions  could  tell  his 
altitude  at  once,  form  no  exception  to  this  statement,  for  they  were  cal- 
culated upon  the  theory  that  it  is  possible,  by  the  application  of  Ma- 
riotte's  law,  to  determine  how  thick  a  layer  of  the  atmosphere  must  be, 
at  different  altitudes,  to  just  balance  a  column  of  mercury  a  hundredth 
of  an  inch  in  height. 

The  numerical  coefficient  in  the  barometric  formula  can  be  obtained  in 
two  ways.  The  empirical  method  consists  in  comparing  the  heights  de- 
termined by  exact  trigonometrical  operations  with  those  obtained  from 
observations  of  the  barometer.  In  these  comparisons  this  coefficient  is 
regarded  as  an  unknown  quantity,  and  made  to  satisfy  the  condition  that 
the  two  measurements  shall  be  equal.  In  the  second  method,  which  is 

*  See  Gilbert's  Annalen  der  Physik,  Band  XXXVI.  1810.     pp.  150-167. 


INTRODUCTORY.  15 

more  direct,  the  coefficient  is  deduced  from  a  comparison  of  the  specific 
gravities  of  air  and  mercury,  but  it  is  evidently  subject  to  any  inaccu- 
racies with  which  these  quantities  are  affected,  and  can  take  no  account 
of  possible  differences  in  the  constitution  of  the  upper  atmosphere,  which 
might  affect  the  ratio  existing  between  the  weights  of  equal  volumes  of 
these  substances  at  high  elevations.  The  coefficient  derived  from  theo- 
retical considerations  alone  giving  results  which  were  too  small,  Laplace 
adopted  the  empirical  value  determined  by  Eamond  from  measurements 
made  in  the  Pyrenees.  The  mountain  selected  for  these  measurements 
was  the  Pic  du  Midi  de  Bigorre,  a  peak  which  rises  to  an  altitude  of 
over  nine  thousand  feet  above  the  level  of  the  sea,  and  which  was  ex- 
tremely well  situated  for  experiments  of  this  kind,  being  comparatively 
isolated,  and  not  being  separated  by  any  intervening  ridge  from  the  sta- 
tion on  the  plain,  eight  thousand  feet  below,  where  the  corresponding 
observations  were  taken.*  The  observations  were  taken  in  the  latter  part 
of  September,  1803,  and,  in  all  instances,  near  the  middle  of  the  day. 
It  is  evident  that  a  coefficient  thus  determined  would  be  rigorously  exact 
only  for  measurements  under  similar  conditions.  If  a  mountain  in  a  dif- 
ferent latitude  had  been  chosen,  or  if  a  different  month  or  a  different 
hour  of  the  day  had  been  selected,  or  if  the  measurements  had  been  made 
upon  stormy  instead  of  upon  pleasant  days,  the  numerical  value  of  the 
coefficient  would  doubtless  have  been  different;  how  much  different  it  is 
needless  now  to  inquire.  It  is  sufficient  to  know  that  the  number  finally 
adopted  by  Laplace,  and  published  in  the  "Me"canique  Celeste,"  was  the 
one  which  seemed  most  accurate,  on  the  supposition  that  the  lower  ba- 
rometer was  at  the  level  of  the  sea,  in  latitude  45°,  and  that  the  tem- 
perature of  the  air  was  that  of  melting  ice.  What  effect  the  climatic 
conditions  prevailing  in  the  region  of  the  Pyrenees  would  have  upon  this 
coefficient  it  is  not  possible  to  say,  but  it  would  not  be  strange  if  the 
coefficient  had  to  be  increased  or  diminished  in  order  to  attain  the  best 
results  in  regions  where  the  climate  differed  much  from  that  of  the  Pyr- 
enees. This  view  was,  indeed,  advanced  and  defended  by  the  German 
astronomer,  Lindenau,f  who,  in  the  construction  of  his  tables,  which  were 


*  Ramond's  Memoires  sur  la  Foramle  Barometrique.     Paris,  1811.     p.   5. 
t  Lindenau's  Tables  Barometriques.     Gotha,  1809.     p.  xxxvii. 


UNIVERSITYo/miFORNIA 


COLLEGE  o/*  MINING 


DEPARTMENTAL 


BEQUEST  OF 


5AM  UELBENEDICTCHRISTY 

PROFESSOR  OF 

MINING  AND   METALLURGY 

1885-1914 


:      ••  -; 

;:  mim 


BERKELEY 

LIBRARY 

UNIVERSITY    OF 
CALIFORNIA 


BAROMETRIC  HYPSOMETRY, 


DOCUMENTS  DEPARTMENT 

APR  28 


LIBRARY 
UNIVERSITY  OF  CAU*0*MIA 


/9 


GEOLOGICAL  SURVEY  OF  CALIFORNIA, 

J.  D.  WHITXEY,  STATE  GEOLOGIST. 


CONTRIBUTIONS 


TO 


BAROMETRIC  HYPSOMETRY: 


WITH    TABLES    FOR    USE 
IN   CALIFORNIA. 


PUBLISHED  BY  AUTHORITY  OF  THE  LEGISLATURE. 
1874. 


UNIVERSITY  PRESS:  WELCH,  BIGELOW,  &  Co., 
CAMBRIDGE. 


C3 


PEEFATORY  NOTE. 


"T  PAYING  been,  for  more  than  twenty-five  years,  almost  constantly 
-^ —  employed  in  geological  surveys  of  our  Western  States,  I  have  had 
occasion  to  use  the  barometer  quite  extensively  as  a  hypsometrical  in- 
strument. As  early  as  1847,  being  engaged  in  determining  the  height  of 
points  along  the  south  shore  of  Lake  Superior,  I  became  convinced  that 
there  were  sources  of  error  in  our  barometrical  work  which  had  not  been 
sufficiently  taken  into  account;  and  by  repeated  measurements  of  a  num- 
ber of  elevations  at  different  seasons  and  hours,  I  arrived  at  the  conclu- 
sion that  our  results  were  always  lower  in  cold  weathsr,  or  at  morning 
and  evening,  than  they  were  in  warmer  weather  or  .towards  noon.  For 
some  years  after  this  my  field  of  labor  was  among  the  prairies  of  the 
Mississippi  Valley,  where  there  was  little  occasion  for  hypsometrical  work, 
and  the  subject  of  the  uncertainties  and  perplexities  of  barometrical  de- 
terminations of  heights  was  for  a  time  dismissed  from  my  thoughts. 

Later,  however,  on  taking  charge  of  the  Geological  Survey  of  Califor- 
nia, where  the  barometer  became  again  an  instrument  of  the  greatest 
importance,  and  indeed  an  indispensable  companion  in  our  field-work,  the 
same  difficulties  which  had  been  met  with  on  Lake  Superior  began  again 
to  be  noticed,  and  to  call  for  investigation.  Learning,  however,  that  Col- 
onel Williamson  was  engaged  in  making,  under  the  authority  of  the 
United  States  Engineer  Bureau,  a  series  of  observations  with  a  view  to 
the  publication  of  an  elaborate  work  on  the  use  of  the  barometer  as  a 
hypsometrical  instrument,  it  was  deemed  best  to  defer  undertaking  any 


4  PREFATORY  NOTE. 

researches  of  our  own  until  after  his  had  been  completed,  and  the  results 
printed.  The  Geological  Survey,  meanwhile,  lent  such  aid  to  this  distin- 
guished officer  as  it  was  in  our  power  to  furnish.  On  the  publication  of 
his  volume,  however,  it  was  found  that,  although  thorough  and  valuable 
as  far  as  it  went,  it  did  not  fully  meet  our  needs,  but  that  the  investi- 
gation required  to  be  carried  a  little  further,  in  order  that  results  might 
be  had  which  could  be  put  to  practical  use. 

The  great  expense  of  the  determination  by  the  spirit-level  of  the  ele- 
vation of  a  number  of  points  in  the  Sierra  Nevada  between  its  base  and 
summit  was  an  obstacle  to  our  commencing  the  proposed  work;  but  the 
completion  of  the  Central  Pacific  Eailroad  seemed  to  remove  this  diffi- 
culty, by  giving  us  not  only  pretty  accurately  the  elevation  desired,  but 
also  a  chance  for  permanent  stations  and  good  observers  among  the  tele- 
graph operators  employed  at  the  different  offices  along  the  line.  It  was 
therefore  decided  that  three  points  should  be  selected,  and  observations 
made  three  times  a  day  at  each,  for  a  period  of  one  year,  and,  if  possi- 
ble, for  three,  as  is  fully  set  forth  in  the  second  chapter  of  this  little 
work.  Here  I  must  take  occasion  to  return  sincere  thanks  to  Leland 
Stanford,  President  of  the  Central  Pacific  Railroad,  for  facilities  furnished 
us  during  this  series  of  observations  ;  for,  without  his  help,  it  would 
hardly  have  been  possible  for  us  to  carry  on  the  investigation. 

A  fourth  station  at  an  elevation  of  twelve  thousand  to  fourteen  thou- 
sand feet  was  very  desirable;  but  this  great  enlargement  of  the  plan  was 
entirely  beyond  our  means,  and  we  were  obliged  to  content  ourselves 
with  the  summit  station  of  the  railroad  as  our  highest  point. 

At  the  time  this  investigation  was  commenced  I  had  very  little  ac- 
quaintance with  anything  which  had  been  done  by  others  in  the  direc- 
tion of  our  own  line  of  inquiry.  It  did  not  appear,  however,  that  any 
such  tables  of  correction  as  we  hoped  to  prepare  had  ever  come  into 
practical  use ;  and  it  became  more  and  more  evident,  as  our  work  went 
on,  that,  in  all  probability,  our  results  would  be  of  value  to  observers  on 
the  Pacific  coast.  Books  of  reference  were  not  to  be  obtained  there  ;  but 


PREFATORY  NOTE.  5 

now  that  we  have  procured  them,  —  and  not  without  considerable  search 
in  Europe,  —  and  know  that  others  have  gone  over  very  nearly  the  same 
ground  that  we  have,  it  appears  none  the  less  desirable  that  our  investi- 
gations should  have  been  made,  or  that  they  should  now  be  published. 
Indeed,  we  have  at  present  more  confidence  than  ever  in  their  value,  al- 
though less  entitled  to  claim  merit  for  originality  than  we  had  supposed 
ourselves  to  be;  for  we  now  perceive  very  clearly  that  each  country  and 
climate  demands  something  similar  to  that  which  we  have  attempted  to 
do  for  California,  if  the  hypsometric  data  obtained  by  the  use  of  the 
barometer  are  to  be  rendered  as  accurate  as  possible,  which  every  one 
will  admit  to  be  highly  desirable.  It  is  indeed  probable  that  the  Pacific 
coast  is  one  of  those  regions  where  the  barometric  results  are  most  liable 
to  those  discrepancies  which  have  been  the  subject  of  our  investigations, 
and  that  on  this  account  our  work  has  been  particularly  needed  there; 
but  it  is  clear  that  the  uncertainties  in  question  cannot  anywhere  be 
neglected,  and  that  by  the  use  of  suitable  tables  of  correction  for  the 
hour  of  the  day  and  the  season  of  the  year,  the  accuracy  of  the  barom- 
eter as  a  hypsometric  instrument  may  be  very  considerably  increased. 

Professor  W.  H.  Pettee,  of  Harvard  University,  has  had  charge  of  the 
onerous  labor  of  the  reduction  and  computation  of  the  observations ;  and 
this  little  volume,  prepared  by  him  from  the  data  collected  by  the  Sur- 
vey, owes  a  large  share  of  its  value  to  his  accurate  and  persevering  work 
upon  it.  With  his  assistance  a  very  complete  library  of  works  devoted 
to  the  barometer  has  been  accumulated,  and  in  every  case  the  references 
here  given  have  been  verified  by  consultation  of  the  original  authorities. 
It  is  believed  that  nothing  of  importance  connected  with  the  present 
inquiry  can  have  escaped  our  notice,  and  that  in  the  concluding  chapter 
of  this  work  a  pretty  complete  resume  of  the  labors  of  other  investigators 
has  been  presented. 

J.  D.  W. 

CAMBRIDGE,  MASS.,  May  28,  1874. 


TABLE    OF    CONTENTS. 


CHAPTER   I. 

INTRODUCTORY. 

Principles  of  barometric  measurements,  —  imperfection  of  the  earlier  formulae,  —  Laplace's  com- 
plete formula,  9  ;  different  estimates  of  the  value  of  barometrical  work,  —  Guyot  quoted,  10  ; 
practical  result  of  Guyot's  publication,  — views  of  geologists  and  geographers,  11  ;  use  of 
barometer  upon  the  California  Survey, — discrepancies  observed,  —  special  investigation  de- 
cided upon,  12  ;  early  investigators  in  this  field,  — the  four  terms  of  Laplace's  formula, — 
their  possible  imperfections,  — a  fifth  term  added,  13  ;  transformations  of  the  formula  to  facili- 
tate computations,  —  Benzenberg's  tables  —  two  methods  of  obtaining  the  numerical  coeffi- 
cient, 14;  Ramond's  empirical  determination  of  the  coefficient, — Lindenau's  change  of  its 
value,  15  ;  Regnault's  investigations  and  Plantamour's  change  of  the  coefficient,  —  William- 
son's study  of  the  coefficient,  — supposition  of  condition  of  equilibrium  in  the  atmosphere,  16  ; 
Benzenberg's  criticism  of  the  pressure  term  and  his  table  of  corrections  shown  to  be  un- 
founded, 17  ;  Ohm's  supposed  improvement  of  the  formula  by  substituting  a  conical  for  a 
cylindrical  air  column,  —  necessity  of  a  correction  for  temperature  and  for  moisture,  18  ;  law 
of  decrease  of  temperature  with  altitude  not  known,  —  Laplace's  hypothesis,  —  Lindenau's 
proposed  change,  19  ;  Baeyer's  discussion  of  the  formula,  20  ;  Laplace's  mode  of  correcting 
for  the  effects  of  moisture,  —  shown  to  be  erroneous,  —  Bessel's  formula,  21  ;  formulae  of 
Plantamour,  Williamson,  Bauernfeind,  Renny,  and  Riihlmann,  22  ;  difficulty  in  the  way  of 
using  formulae  with  special  correction  for  moisture,  —  table  showing  the  effect  of  a  separate 
correction  for  moisture  in  Switzerland  and  in  California,  23  ;  discrepancy  not  entirely  re- 
moved, —  table  giving  computed  difference  of  altitude  between  Geneva  and  St.  Bernard,  24. 


CHAPTER    II. 

DETAILED   ACCOUNT   OF   THE   INVESTIGATION   IN   CALIFORNIA. 

Object  of  the  investigation,  —  its  necessity,  25  ;  Williamson's  work,  —  accumulation  of  observa- 
tions, —  instruments  used,  26  ;  stations  at  which  observations  were  taken,  —  observers  at 
Sacramento  and  at  Colfax,  —  the  monthly  returns  from  those  stations,  27  ;  observations  at 
Summit,  —  names  of  the  observers,  28  ;  relative  position  of  the  stations  and  their  latitudes,  — 
advantages  of  Sacramento  as  a  meteorological  station,  29  ;  of  Colfax,  —  difficulties  in  the  way 
of  getting  good  observations  at  Summit,  —  hours  of  observation,  30  ;  reduction  of  the  observa- 
tions begun,  —  reason  for  not  including  the  readings  of  the  psychrometer,  31  ;  tables  of  the 
mean  height  of  barometer  and  thermometer  for  three  years  at  the  three  stations,  32  -  34  ; 
choice  of  hypsometrical  tables  to  be  used,  —  construction  of  Tables  I.  -XII.,  35  ;  conclusions 
drawn  from  these  twelve  tables,  36,  37  ;  explanation  of  Tables  XIII.  -XIX.,  38  ;  construction 
of  Tables  XX.  -  XXII.,  39  ;  construction  of  Tables  XXIII.  -  XXV.,  —  comparative  results,  40  ; 


TABLE   OF  CONTENTS. 

use  to  be  made  of  the  tables  for  foot-hills  and  mountains,  41  ;  desirability  of  tables  for 
higher  altitudes, — stations  in  Colorado,  42;  use  of  tables  for  points  of  intermediate  alti- 
tude, —  illustrations  of  the  use  of  the  tables,  43  ;  table  showing  altitude  of  Yosemite  Valley, 
44  ;  unfavorable  character  of  this  example,  45  ;  tables  showing  altitudes  of  camp  in  Tuolumne 
Canon  and  of  Peregoy's,  46  ;  tables  showing  the  effect  of  taking  the  mean  of  two  days,  —  no 
higher  degree  of  accuracy  ordinarily  attainable,  —  peculiar  value  of  the  barometer,  47  ;  not 
available  for  determining  small  differences  of  altitude,  —  comparison  of  Sacramento  with  San 
Francisco,  —  table,  48  ;  explanation  of  the  result,  —  limitation  of  the  use  of  the  tables,  — 
table  showing  the  computed  difference  of  altitude  between  San  Francisco  and  Colfax,  49  ; 
between  San  Francisco  and  Summit,  50. 


CHAPTER    III. 

RESUME   OF   SIMILAR   INVESTIGATIONS   OUTSIDE   OF   CALIFORNIA. 

Summary  of  the  first  chapter,  —  object  of  the  present  chapter,  51  ;  Kamond's  investigations, 
52-54  ;  D'Aubuisson's  recognition  of  the  annual  period,  55  ;  Homer's  study  of  the  diurnal 
period,  56,  57  ;  Homer's  table  of  corrections,  —  corrections  proposed  by  Bravais,  58  ;  Kaemtz, 
59  ;  Baeyer's  formula  not  free  from  errors,  —  Geneva  and  St.  Bernard  observations,  60  ;  Plan- 
tamour's  investigations,  61  ;  Kenny's  labors,  62  ;  Kenny's  table  of  corrections,  63  ;  compared 
with  Table  XXIV.,  64  ;  Kenny's  conclusions,  65  ;  the  work  of  the  brothers  Schlagintweit  in 
India,  66  ;  Bauernfeind's  investigations  in  Bavaria,  67,  68  ;  Kiihlmann's  study  of  the  diurnal 
and  the  annual  periods,  69-71  ;  conclusion,  72. 

TABLES,  73-88.  


SUPPLEMENTARY    CHAPTER. 

(ADDED    1878.) 

A  PRACTICAL  APPLICATION  OF  THE  TABLES  TO  THE  OBSERVATIONS    OF    THE    YEARS    1870-71, 
AND  A  DISCUSSION  OF  THE  RESULTS  OBTAINED. 

Object  of  the  present  chapter,  89  ;  where  and  by  whom  the  observations  were  taken,  89,  90  ; 
method  of  computation,  90,  91  ;  table  of  altitudes  computed  with  reference  to  different  cor- 
responding stations,  92,  93  ;  remarks  on  this  table,  93  -  96  ;  results  obtained,  96  ;  another 
method  of  testing  the  value  of  the  tables,  96,  97  ;  table  showing  the  range  and  errors  of  the 
unconnected  and  the  corrected  differences  of  altitude  between  two  stations,  98  - 109  ;  remarks 
on  this  table,  110-112  ;  position  of  the  stations  used,  110,  111  ;  results  obtained,  111,  112. 


OHAPTEE   I. 

LNTEODUCTOEY. 

main  principle  underlying  the  method  of  determining  altitudes, 
-L  or  differences  of  altitude,  by  means  of  the  barometer  is  simple,  and 
easily  understood.  From  the  observed  heights  of  the  columns  of  mercury 
in  two  barometers  at  different  altitudes,  but  not  separated  by  any  great 
distance  horizontally,  we  have  at  once  the  weights  of  a  column  of  air 
reaching  from  the  lower  instrument  to  the  outer  limit  of  the  atmosphere, 
and  of  that  portion  of  the  air-column  which  rises  above  the  upper  in- 
strument. The  weight  of  the  column  of  air  between  the  two  instruments 
is  therefore  known;  and  it  would  seem  at  first  sight  as  if  nothing  more 
than  moderate  skill  and  ordinary  care  in  making  the  observations  would 
be  necessary  in  order  to  secure  trustworthy  results,  or,  at  least,  a  very 
close  approximation  to  the  truth.  The  earliest  formulae  proposed  in  this 
connection,  however,  were  necessarily  imperfect.  The  laws  governing  the 
changes  of  density  in  the  atmosphere  as  the  altitude  increases  were  not 
known,  and  it  was  not  possible  to  determine  the  actual  weight  of  a  given 
volume  of  air  with  a  sufficient  degree  of  accuracy. 

Laplace  *  was  the  first  to  propose  a  complete  formula  which  should  take 
account  of  all  the  effects  of  varying  temperature  and  variations  in  the  in- 
tensity of  the  earth's  gravitation  at  different  latitudes  and  at  different  heights 
above  the  surface.  The  theoretical  correctness  of  Laplace's  formula  has  re- 
mained essentially  undisputed,  and  yet  there  is  a  wide  difference  of  opinion, 
even  among  those  best  qualified  to  judge,  as  to  the  degree  of  accuracy  actu- 
ally attainable  in  barometric  measurements  of  altitude.  The  prevalent  idea 
among  civil  engineers  is,  that  the  barometer  is  not  a  trustworthy  instru- 

*  Mecanique  Celeste,  Tom.  IV.  pp.  289  -  293.     Paris,  1805. 


10  BAROMETRIC  HYPSOMETRY. 

merit  in  comparison  with  the  spirit-level;  and  there  is  undoubtedly  con- 
siderable ground  for  this  belief.  When  the  heights  of  important  points 
determined  barometrically  by  different  observers,  at  different  seasons  of 
the  year,  and  under  different  meteorological  conditions,  are  compared  with 
each  other,  the  discrepancies  are  frequently  much  too  great  to  be  ac- 
counted for  by  any  errors  of  observation.  It  would  seem  as  if  the  method 
or  the  formula  must  be  at  fault. 

On  the  other  hand,  the  impression  given  by  the  text-books  generally 
in  use  in  the  colleges  and  scientific  schools  of  the  country  is,  that  it  is 
only  necessary  to  multiply  observations  and  take  the  mean  of  the  results 
in  order  to  attain  to  any  desired  degree  of  accuracy ;  and  there  is  no  doubt 
that  the  publication  by  the  Smithsonian  Institution  of  the  well-known 
tables  for  the  use  of  meteorological  observers,  prepared  by  Professor  Guyot, 
has  contributed  largely  to  the  very  favorable  opinion  in  which  the  barom- 
eter is  held  in  many  quarters. 

In  the  introduction  to  his  table  arranged  for  English  measures  Professor 
Guyot  has  given  a  number  of  examples,  in  which  the  results  of  the  com- 
putation of  barometric  observations  are  compared  with  those  obtained  by 
means  of  the  spirit-level  or  from  trigonometrical  calculations,  and  the 
coincidence  is  in  all  cases  quite  remarkable,  —  amounting,  in  fact,  almost 
to  identity.  His  words  are  as  follows  (Series  D,  page  34) :  "  The  close 
agreement  of  the  determinations  furnished  by  Laplace's  formula,  in  baro- 
metrical measurements  carefully  conducted,  made  in  favorable  circum- 
stances and  during  the  warm  season,  with  those  obtained  from  repeated 
trigonometrical  observations  or  by  the  spirit-level,  strongly  testifies  in 
favor  of  its  general  correctness."  He  then  gives  several  examples  of 
wonderfully  close  agreement  of  barometrical  with  trigonometrical  results, 
and  adds :  "  These  figures  show  conclusively  that  when  the  errors  which 
may  arise  from  the  great  variability  of  the  data  furnished  by  the  instru- 
ments have  been  removed  by  a  repetition,  in  various  states  of  the  atmos- 
phere, and  by  a  proper  combination  of  simultaneous  observations  at  sta- 
tions not  too  distant  from  each  other,  those  which  remain  and  may  be 
attributed  to  the  formula  cannot  be  considerable.  But,  on  the  other  hand, 
we  have  no  right  to  expect  such  results  from  single  observations,  taken 
perhaps  in  unsettled  weather,  without  paying  any  regard  to  the  time  of 
the  day  at  which  they  were  made,  to  the  .distance  or  the  non-simulta- 


INTRODUCTORY.  11 

neity  of  the  corresponding  observations,  or  to  other  unfavorable  circum- 
stances." Of  the  nature  of  the  unfavorable  circumstances  alluded  to,  or 
of  the  proper  time  of  day,  or  of  the  character  of  the  favorable  circum- 
stances required  to  bring  about  such  favorable  results,  no  hint  whatever 
is  here  given.  The  most  that  could  be  inferred  would  be  that  it  is  neces- 
sary to  make  the  measurements  "in  the  warm  season,"  and  repeat  the 
observations  "  in  various  states  of  the  atmosphere."  The  remarkably  well- 
agreeing  results  given,  however,  were  all  computed  from  observations  taken 
on  a  single  day,  excepting  in  one  case  where  the  observations  extended 
over  parts  of  two  days.  The  practical  result  has  been  that  it  is  almost 
universally  taught,  in  this  country  at  least,  that  care  and  repetition  of 
the  observations  during  a  good  part  of  a  day  will  be  sufficient  to  secure 
satisfactory  results.  It  is  true  that  on  pages  80  —  82  of  the  same  series 
Professor  Guyot  has  given  tables  of  corrections,  in  French  measures,  to  be 
applied  for  different  hours  of  the  day  to  the  approximate  results  obtained 
in  the  ordinary  way,  and  thus  admitted  the  existence  of  important  sources 
of  error ;  but  these  corrections  he  neglected  to  take  into  account  in  his  own 
measurements,  and  thus  contributed  largely  to  the  belief  that  they  were 
less  important  than  they  really  are. 

Intermediate  between  these  extremely  favorable  and  extremely  unfavor- 
able views  belong  the  opinions  of  the  great  majority  of  geologists  and 
geographers,  who,  neither  requiring  nor  expecting  extreme  accuracy,  find 
the  barometer  an  indispensable  instrument  upon  their  surveys  and  recon- 
noissances,  since  with  its  aid  they  are  enabled  to  secure  results  suffi- 
ciently accurate  for  their  purposes,  while  without  it  they  would  have  no 
results  at  all,  —  the  determination  of  differences  of  altitude  with  the  spirit- 
level,  if  the  distances  are  great,  being  a  very  laborious  and  costly  oper- 
ation. A  sufficient  proof,  indeed,  if  anything  additional  is  needed,  that 
the  barometer  is  a  hypsometric  instrument  of  great  value,  is  found  in 
the  fact  that  it  has  been  very  widely  used  in  all  parts  of  the  world,  not 
only  for  measuring  high  mountains,  but  also  for  determining  the  limits 
of  the  distribution  of  plants,  the  relative  position  of  geological  formations, 
and  the  most  available  routes  for  long  lines  of  railway  across  rough  and 
thinly  settled  regions.  It  was  entirely  by  means  of  trial  lines  run  with 
the  barometer  that  the  easiest  route  for  the  Central  Pacific  Eailroad  was 
found. 


12  BAROMETKIC  HYPSOMETRY. 

The  value  of  the  barometer  as  a  field  instrument  has  been  seen  to 
great  advantage  during  the  progress  of  the  California  Survey.  It  was  evi- 
dent at  the  outset,  owing  to  the  great  size  of  the  State,  its  mountainous 
character,  and  the  fact  that  so*  large  a  portion  was  practically  unexplored, 
that  the  barometer  would  have  to  be  a  chief  dependence,  and  in  many 
cases  the  sole  means  available,  in  procuring  the  necessary  data  for  the 
determination  of  important  geological  and  topographical  questions ;  and, 
as  the  work  has  gone  on,  it  has  grown  more  and  more  clear  that,  with- 
out its  aid,  much  that  has  been  accomplished  would  have  remained  un- 
done, or  even  unattempted.  At  the  same  time  it  has  been  well  understood 
that  the  results  obtained  in  this  way  were  to  be  regarded  only  as  approx- 
imations, varying  more  or  less  from  the  truth,  —  the  amount  of  variation 
depending  upon  certain  unknown  or  imperfectly  known  conditions. 

It  was  found,  for  instance,  that  observations  taken  in  midsummer  indi- 
cated a  greater  difference  of  altitude  between  two  given  points  than  sim- 
ilar observations  taken  in  the  spring  or  fall;  that  the  results  obtained 
from  morning  or  evening  observations  differed  from  those  obtained  from 
midday  observations,  the  latter  being  invariably  the  greater;  and  that 
the  difference  of  altitude  between  two  points  determined  directly  was  apt 
to  differ  from  that  obtained  with  aid  of  one  or  more  intermediate  sta- 
tions; but  it  was  not  possible  to  tell  which  of  these  discordant  results 
was  the  most  trustworthy.  The  discrepancies  were  obvious ;  their  expla- 
nation and  correction  were  matters  of  great  difficulty.  Questions  concern- 
ing the  probabilities  of  error  in  using  the  barometer  were  of  constant 
"recurrence;  and  it  was  at  length  determined  to  enter  upon  an  extended 
investigation,  with  the  view  of  ascertaining,  if  possible,  the  probable  error 
of  any  single  observation,  or  of  constructing  a  table  of  corrections  to  be 
applied  to  the  results  obtained  under  different  conditions.  A  detailed 
account  of  the  method  of  procedure  adopted  in  this  investigation  will  be 
given  further  on;  but  first  it  will  be  necessary  to  understand  clearly  the 
exact  conditions  of  the  problem. 

The  problem  is  not  new.  Discrepancies  similar  to  those  mentioned 
above  have  attracted  attention  wherever  any  extended  use  of  the  barom- 
eter in  measuring  altitudes  has  been  attempted,  and  the  subject  has  been 
repeatedly  examined  from  a  great  variety  of  standpoints.  During  the 
century  and  a  half  which  followed  the  famous  experiment  of  Pascal,  in 


INTRODUCTORY.  13 

1648,  numerous  formulae  were  proposed  to  facilitate  the  barometric  deter- 
mination of  altitudes,  in  connection  with  which  the  names  of  Mariotte, 
Halley,  Deluc,  Playfair,  and  Schuckburgh  were  prominent,  but  which  must 
now  be  regarded  as  only  having  paved  the  way  for  the  more  complete 
formula  of  Laplace.  The  discordant  results  obtained  when  this  formula, 
or  some  modification  of  it,  has  been  employed  are  what  we  have  to  deal 
with. 

Laplace's  original  formula  comprised  four  terms,  which  may  be  desig- 
nated as  the  pressure  term,  including,  as  is  usual,  the  principal  numerical 
coefficient ;  the  temperature  term ;  the  correction  for  latitude ;  and  the 
correction  for  the  change  in  the  height  of  the  mercury  column  in  the 
barometer  caused  by  the  variation  in  the  intensity  of  gravity  with  increase 
of  altitude.  "The  corrections  depending  upon  the  latitude  and  upon  the 
variation  of  gravity  are  very  small;  but  as  they  really  exist,  it  is  best  to 
notice  them,  so  as  to  leave  in  the  calculation  no  other  imperfections  than 
those  which  arise  from  the  inevitable  errors  of  observation;  or  from  the 
effect  of  the  unknown  attractions  of  the  mountains;  or  from  the  hygro- 
metrical  state  of  the  air,  which  ought  to  be  noticed;  or,  finally,  from  the 
error  arising  from  the  use  of  the  hypothesis  relative  to  the  law  of  the 
diminution  of  heat."  *  This  quotation  will  be  sufficient  to  show  what 
Laplace  considered  as  the  possible  imperfections  of  his  formula,  and  to 
give  us  a  hint  as  to  the  probable  character  of  the  modifications  which 
would  be  introduced  by  subsequent  investigators.  So  far  as  the  correc- 
tions for  latitude  and  for  variation  of  gravity  are  concerned,  little  need 
be  said.  Their  numerical  values  would  have  to  be  changed,  it  is  true, 
whenever  improved  methods  of  research  should  make  possible  more  accu- 
rate determinations  of  the  values  of  the  physical  constants  involved. 
But,  as  the  only  constants  to  be  considered  in  this  connection  are  the 
length  of  a  seconds  pendulum  and  the  mean  radius  of  the  earth,  it  is 
evident  that  the  changes,  when  made,  could  have  only  a  very  small  effect 
upon  the  final  result,  —  the  values  of  these  constants  already  adopted 
leaving  but  little  to  be  desired  in  the  way  of  accuracy.  The  addition  by 
Oltmanns  of  a  fifth  term,  to  introduce  a  small  correction  depending  upon 
the  height  of  the  lower  barometer  above  the  sea-level,  requires  also  only 
a  passing  mention. 

*  Mecanique  Celeste,  Bowditch's  translation,  Vol.  IV.  p.  571. 


14  BAROMETRIC  HYPSOMETRY. 

The  pressure  term  and  the  temperature  term,  therefore,  are  the  only  ones 
remaining,  subject  to  any  essential  modification;  and  in  what  follows  it 
will  be  seen  how  varied  in  character  the  modifications  proposed  have  been. 

It  is  necessary  to  observe,  however,  that  many  of  the  changes  which 
the  formula  has  undergone,  though  of  great  importance  in  themselves, 
were  really  less  radical  than  would  appear  at  first  sight.  As  first  pub- 
lished the  formula  was  ill-adapted  for  purposes  of  calculation.  The  oper- 
ations required  were  complex,  and  the  work  was  tedious.  Transformations 
were  therefore  made  with  the  view  of  reducing  the  amount  of  numerical 
computation,  or  of  securing  a  tolerable  approximation  with  very  little 
labor,  or  of  adapting  the  formula  to  different  standards  of  measure,  but 
not  necessarily  connected  with  the  idea  of  remedying  any  of  its  deficien- 
cies or  increasing  its  theoretical  or  practical  accuracy.  Hypsometrical 
tables  of  greater  or  less  extent,  some  requiring  and  some  avoiding  the 
use  of  logarithms,  and  giving  results  in  English,  French,  or  other  units 
of  measure,  have  been  published  from  time  to  time,  but  in  almost  all 
cases  the  criterion,  according  to  which  the  ultimate  value  of  the  table 
was  to  be  judged,  was  the  more  or  less  close  agreement  of  the  results 
with  those  which  would  have  been  obtained  if  the  formula  of  Laplace 
had  been  applied  rigorously.  The  special  formula  upon  which  each  set 
of  tables  was  based  might  differ  widely  in  form,  though  not  in  substance, 
from  that  of  Laplace.  The  tables  proposed  by  Dr.  Benzenberg,*  by  aid 
of  which  an  observer  performing  a  few  simple  additions  could  tell  his 
altitude  at  once,  form  no  exception  to  this  statement,  for  they  were  cal- 
culated upon  the  theory  that  it  is  possible,  by  the  application  of  Ma- 
riotte's  law,  to  determine  how  thick  a  layer  of  the  atmosphere  must  te, 
at  different  altitudes,  to  just  balance  a  column  of  mercury  a  hundredth 
of  an  inch  in  height. 

The  numerical  coefficient  in  the  barometric  formula  can  be  obtained  in 
two  ways.  The  empirical  method  consists  in  comparing  the  heights  de- 
termined by  exact  trigonometrical  operations  with  those  obtained  from 
observations  of  the  barometer.  In  these  comparisons  this  coefficient  is 
regarded  as  an  unknown  quantity,  and  made  to  satisfy  the  condition  that 
the  two  measurements  shall  be  equal.  In  the  second  method,  which  is 

*  See  Gilbert's  Annalen  der  Physik,  Band  XXXVI.  1810.     pp.  150-167. 


INTRODUCTORY.  15 

more  direct,  the  coefficient  is  deduced  from  a  comparison  of  the  specific 
gravities  of  air  and  mercury,  but  it  is  evidently  subject  to  any  inaccu- 
racies with  which  these  quantities  are  affected,  and  can  take  no  account 
of  possible  differences  in  the  constitution  of  the  upper  atmosphere,  which 
might  affect  the  ratio  existing  between  the  weights  of  equal  volumes  of 
these  substances  at  high  elevations.  The  coefficient  derived  from  theo- 
retical considerations  alone  giving  results  which  were  too  small,  Laplace 
adopted  the  empirical  value  determined  by  Eamond  from  measurements 
made  in  the  Pyrenees.  The  mountain  selected  for  these  measurements 
was  the  Pic  du  Midi  de  Bigorre,  a  peak  which  rises  to  an  altitude  of 
over  nine  thousand  feet  above  the  level  of  the  sea,  and  which  was  ex- 
tremely well  situated  for  experiments  of  this  kind,  being  comparatively 
isolated,  and  not  being  separated  by  any  intervening  ridge  from  the  sta- 
tion on  the  plain,  eight  thousand  feet  below,  where  the  corresponding 
observations  were  taken.*  The  observations  were  taken  in  the  latter  part 
of  September,  1803,  and,  in  all  instances,  near  the  middle  of  the  day. 
It  is  evident  that  a  coefficient  thus  determined  would  be  rigorously  exact 
only  for  measurements  under  similar  conditions.  If  a  mountain  in  a  dif- 
ferent latitude  had  been  chosen,  or  if  a  different  month  or  a  different 
hour  of  the  day  had  been  selected,  or  if  the  measurements  had  been  made 
upon  stormy  instead  of  upon  pleasant  days,  the  numerical  value  of  the 
coefficient  would  doubtless  have  been  different;  how  much  different  it  is 
needless  now  to  inquire.  It  is  sufficient  to  know  that  the  number  finally 
adopted  by  Laplace,  and  published  in  the  "Me"canique  Celeste,"  was  the 
one  which  seemed  most  accurate,  on  the  supposition  that  the  lower  ba- 
rometer was  at  the  level  of  the  sea,  in  latitude  45°,  and  that  the  tem- 
perature of  the  air  was  that  of  melting  ice.  What  effect  the  climatic 
conditions  prevailing  in  the  region  of  the  Pyrenees  would  have  upon  this 
coefficient  it  is  not  possible  to  say,  but  it  would  not  be  strange  if  the 
coefficient  had  to  be  increased  or  diminished  in  order  to  attain  the  best 
results  in  regions  where  the  climate  differed  much  from  that  of  the  Pyr- 
enees. This  view  was,  indeed,  advanced  and  defended  by  the  German 
astronomer,  Lindenau,f  who,  in  the  construction  of  his  tables,  which  were 


*  Ramond's  Memoires  sur  la  Formule  Barometrique.     Paris,  1811.     p.  5. 
t  Limlenau's  Tables  Barometriques.     Gotha,  1809.     p.  xxxvii. 


16  BAROMETRIC  HYPSOMETRY. 

intended  more  especially  for  use  in  Germany,  adopted  a  value  differing 
to  some  extent  from  that  fixed  by  Ramond.  The  elaborate  investigations 
of  Eegnault,  in  the  course  of  which  the  specific  gravities  of  air  and  mer- 
cury were  ascertained  to  a  greater  degree  of  accuracy  than  ever  before, 
led  also  to  some  modifications  of  the  barometric  coefficient;  a  new  value, 
somewhat  larger  than  Ramond's,  being  adopted  by  Plantamour*  in  his 
tables,  which,  adapted  to  English  measures,  have  been  published  by  Col- 
onel Williamson  in  the  appendix  to  his  treatise  "  On  the  Use  of  the 
Barometer."  f 

The  changes,  however,  in  the  numerical  coefficient  have  been  neither 
great  in  amount  nor  of  such  a  nature  as  to  cause  the  discordant  results 
which  have  been  referred  to  above  to  disappear ;  and  it  is  evident  that 
the  cause  of  the  difficulty  must  be  sought  elsewhere  than  in  the  erro- 
neous estimations  of  this  quantity.  It  is  not  unlikely  that  the  coefficient 
which  would  give  the  best  results  in  Europe  or  in  the  eastern  part  of 
the  United  States  would  not  be  the  one  best  adapted  for  the  climate  of 
California ;  but  it  is  equally  improbable  that  any  important  advantage 
would  be  gained  by  any  attempt  to  determine  a  special  coefficient  for 
use  on  the  Pacific  coast.  The  results  of  Colonel  Williamson's  examina- 
tion J  into  the  possibility  of  assigning  values  to  the  barometric  constants 
which  shall  give  a  "correct  value  to  the  mean  difference  of  altitude,  and 
at  the  same  time  make  the  computed  results  the  same  for  all  the  months," 
can  well  be  taken  as  conclusive  in  this  respect.  The  substitution  of  a 
coefficient  based  upon  the  best  modern  determinations  of  specific  gravity 
in  the  place  of  the  less  accurate  number  adopted  by  Laplace  is  an  ad- 
vantage, but  does  not  bring  the  results  obtained  under  diverse  atmos- 
pheric conditions  into  any  better  accord  with  each  other. 

The  other  portion  of  the  pressure  term  of  Laplace's  formula  depends 
upon  the  supposition  that  the  atmosphere  is  in  a  condition  of  equilib- 
rium, and  that  the  column  of  mercury  in  the  barometer  is  balanced  by 
a  column  of  air  reaching  to  the  outer  limit  of  the  atmosphere.  Were  all 
the  forces  which  tend  to  cause  motion  in  the  atmosphere  to  cease  acting, 

*  Memoires  de  la  Societe  de  Physique  et  d'Histoire  Naturelle  de  Geneve.  Tom.  XIII. 
1852.  pp.  53  note,  and  66. 

t  Professional  Papers  of  the  Corps  of  Engineers,  TJ.  S.  Army,  No.  15.     1867. 
t  Pages  221  -  228  of  the  work  just  cited. 


INTRODUCTORY.  17 

this  supposed  condition  of  equilibrium  would  soon  be  attained;  but  so 
long  as  these  forces  act  there  must  always  be  a  greater  or  less  inaccuracy 
in  the  supposition,  and  a  corresponding  error  in  the  results  obtained  from 
using  the  formula.  This  source  of  error  cannot  be  avoided  entirely,  —  at 
least  not  from  any  theoretical  considerations ;  and  the  only  resource  left 
us  is  to  reject  or  to  assign  less  weight  to  observations  taken  at  times  of 
manifestly  unusual  atmospheric  disturbance.  From  two  other  points  of 
view,  however,  this  term  has  been  supposed  to  be  faulty.  Dr.  Benzen- 
berg,*  applying  Dalton's  law  relating  to  mixtures  of  independent  gases, 
was  convinced  that  each  of  the  four  principal  components  of  the  atmos- 
phere—  namely,  oxygen,  nitrogen,  carbonic  acid,  and  aqueous  vapor  — 
acted  upon  the  barometric  column  independently  of  the  others,  and  that  each 
followed  a  special  law  of  diminution  in  density  with  increase  of  altitude; 
so  that,  to  secure  perfect  results,  four  pressure  terms  were  really  neces- 
sary. The  density  of  the  oxygen  atmosphere  would  decrease  more  rapidly 
than  that  of  the  nitrogen,  and  that  of  the  carbonic  acid  more  rapidly 
than  either ;  and  the  volumes  of  these  gases  in  the  atmosphere  would  thus 
be  proportionally  different  at  different  altitudes.  Instead  of  changing  the 
formula  Benzenberg  prepared  a  table  of  corrections  to  be  applied  to  the 
calculated  results ;  from  which  it  appears  that  the  correction  is  negative 
for  altitudes  less  than  about  thirty-four  thousand  feet  (the  maximum  nu- 
merical value  being  30.9  feet  for  altitudes  of  fifteen  thousand  feet),  and 
positive  for  higher  elevations.  At  first  sight  it  seems  as  if  these  correc- 
tions must  be  made,  but  experiment  has  shown  that  air  collected  at  all 
elevations  above  the  surface,  in  balloon  ascents,  contains  oxygen  and  ni- 
trogen in  almost  precisely  the  same  proportions.  Owing  to  the  extreme 
mobility  and  continued  agitation  of  the  air,  the  state  of  equilibrium  in 
which  the  gases  would  be  arranged  as  Benzenberg  supposed  is  never  at- 
tained, and  consequently  the  necessity  for  the  corrections  vanishes.!  Bes- 
sel's  discussion,:*:  moreover,  of  the  distribution  of  aqueous  vapor  in  the 

*  Gilbert's  Annalen  der  Physik,  Band  XLII.     1812.     pp.   162-176. 

t  In  "  Air  and  Rain,"  London,  1872,  Dr.  Robert  Angus  Smith  cites  a  considerable  num- 
ber of  analyses  in  which  there  seems  to  be  evidence  of  a  slightly  smaller  percentage  of  oxygen 
at  high  altitudes  ;  but  as  this  is  explained  by  an  accompanying  change  in  the  amount  of  car- 
bonic acid  present,  it  cannot  be  regarded  as  justifying  Benzenberg's  corrections.  Compare, 
also,  Herschel's  Meteorology,  p.  21. 

J  Astronomische  Nachrichten,  No.  357  ;  Altona,  1838. 
2 


18  BAROMETRIC   HYPSOMETRY. 

atmosphere  seems  to  be  decisive  against  the  theory,  in  its  fulness,  that 
each  gas  or  vapor  in  the  air,  or  other  mixture  of  gases,  is  exposed  only 
to  the  pressure  of  its  own  particles. 

The  second  criticism  referred  to  is,  that  Laplace  erred  in  considering 
the  effective  air  column  as  a  vertical  cylinder  rather  than  as  a  portion  of 
a  cone  whose  vertex  is  at  the  centre  of  the  earth.  Dr.  Ohm  *  has  the 
credit  of  first  calling  attention  to  this  point.  His  formula  is  simpler  in 
some  respects  than  that  of  Laplace,  and  was  received  with  considerable 
favor,  though  practically,  as  observed  by  Professor  Rogg.f  the  simpli- 
fication amounts  to  no  more  than  doing  away  with  the  correction  for 
the  variation  in  the  intensity  of  gravity.  The  same  observation  was  also 
made  by  Zech,|  in  his  approving  notice  of  Ohm's  formula.  On  the  other 
hand,  Professor  Guldberg  §  of  Christiania  has  wTell  shown  that  it  was  Ohm, 
after  all,  instead  of  Laplace,  who  was  in  fault  by  neglecting,  in  the  de- 
velopment of  his  formula,  the  effects  of  lateral  pressures. 

The  conclusion  is  therefore  inevitable  that  the  pressure  term,  at  least, 
is  to  be  considered  essentially  unalterable,  —  no  change  having  been  pro- 
posed which  can  be  regarded  as  an  improvement  or  as  likely  to  be  of 
service  in  diminishing  the  discrepancies  whose  removal  is  desired. 

There  remains,  then,  the  temperature  term  to  be  examined.  With  every 
increase  of  temperature  the  air  column  expands,  or,  what  amounts  to  the 
same  thing,  a  relatively  larger  portion  of  the  mass  of  the  air  is  found 
above  the  higher  of  two  barometers ;  and  the  difference  of  altitude  between 
them,  as  estimated  from  the  barometric  readings,  will  be  less  than  it 
would  have  been  if  the  air  had  remained  constantly  at  the  lower  tem- 
perature. Any  increase  of  moisture  in  the  atmosphere  would  evidently 
have  a  similar  effect,  —  aqueous  vapor  being  specifically  lighter  than  air. 
Both  these  effects  are  provided  for  by  the  temperature  term,  as  commonly 
written,  which  consequently  becomes  subject  to  change  from  two  points 
of  view. 

The  value  of  the  correction  for  temperature,  independently  of  moisture, 
depends  upon  the  absolute  rate  of  expansion  of  air  by  heat  and  upon 

*  Ohm's  Grundzuge  der  Physik,  Nuremberg,  1853.     pp.  182-193. 

t  See  Schlomilch's  Zeitschrift  fur  Mathematik  und  Physik,  Band  7.     1862.     p.  144. 

J  Astronomische  Nachrichten,  Band  XLI.     1855.     p.  40. 

§  See  Schlomilch's  Zeitschrift,  Band  7,  pp.  359-363. 


INTRODUCTORY.  19 

the  law  which  governs  the  decrease  of  temperature  as  the  altitude  in- 
creases. The  coefficient  of  expansion  of  air  has  been  determined  with 
such  nicety  that  no  further  change  need  be  expected  in  that  direction; 
but  the  case  is  otherwise  with  the  law  of  decrease  of  temperature.  This 
law,  in  fact,  is  not  known;  and  it  seems  scarcely  probable  that  any  law 
will  ever  be  discovered  which  will  explain  all  the  observed  facts.  Were 
the  atmosphere  subject  to  fewer  changes  and  disturbances,  the  chances  for 
detecting  such  a  law  would  be  greater,  and  there  would  be  more  encour- 
agement for  undertaking  an  investigation  with  that  object  in  view.  As 
the  case  stands,  the  only  course  left  is  to  adopt  some  hypothesis  which 
shall  either  simplify  the  formula  or  shall  be  most  in  harmony  with  well- 
grounded  theoretical  considerations.  The  hypothesis  adopted  by  Laplace, 
avowedly  for  the  sake  of  simplicity,  and  justified  by  the  consideration 
that  only  "a  small  interval  in  comparison  with  the  whole  height  of  the 
atmosphere  "  is  in  question,  was  that  the  temperature  decreases  "  nearly 
in  an  arithmetical  progression"  from  one  station  to  the  other;*  which  is 
nearly  the  same  as  supposing  the  temperature  of  the  air  column  to  be 
uniform  throughout,  and  equal  to  the  mean  of  the  temperatures  at  the 
lower  and  upper  stations.  This  hypothesis  also  assumes  that  two  columns 
of  air,  exposed  to  the  same  pressure,  have  the  same  height,  whether  the 
temperature  decreases  or  increases  from  below  upwards,  provided  only  the 
mean  temperature  remains  unaffected. 

Here  seems  to  be  a  weak  point  in  the  formula;  for,  had  any  other 
hypothesis  been  adopted,  a  different  value  for  the  temperature  correction 
would  have  been  obtained.  Lindenauf  was  one  of  the  first  to  suggest  a 
change.  Comparing  the  results  of  his  study  of  the  laws  of  astronomical 
refraction  with  direct  thermometric  observations  at  different  altitudes,  he 
was  led  to  the  conclusion  that  the  temperature  decreases  less  rapidly  in 
the  upper  than  in  the  lower  regions  of  the  atmosphere ;  and,  following  in 
the  track  of  Euler  and  of  Oriani,  he  assumed  that  the  decrease  of  tem- 
perature was  in  accordance  with  an  harmonic  progression,  :£  and  constructed 

*  Mecanique  Celeste,  Bowditch's  Translation,  Vol.  IV.  p.  566. 

+  Tables  Barometriques,  p.  xxxviii. 

J  Three  numbers,  arranged  in  decreasing  order  of  size,  form  an  harmonic  proportion  when  the 
difference  of  the  first  and  the  second  is  to  the  difference  of  the  second  and  the  third  as  the  first 
is  to  the  third.  In  a  series  of  numbers  arranged  as  an  harmonic  progression,  any  three  consecu- 
tive terms  form  an  harmonic  proportion. 


20  BAROMETRIC   HYPSOMETRY. 

his  tables  on  this  basis.  This  hypothesis,  however,  instead  of  simplify- 
ing, complicates  the  formula,  and  contributes  little  or  nothing  to  its  accu- 
racy; for  the  law  of  decrease  of  temperature  is  still  left  in  doubt.  In 
other  respects  the  researches  o'f  Lindeuau  belong  among  the  most  impor- 
tant contributions  to  the  subject  of  barometric  hypsometry,  and  his  his- 
torical sketch  of  the  development  of  the  earlier  formulae  was  much  more 
complete  than  anything  that  had  preceded. 

A  more  important  alteration  in  the  form  of  the  temperature  correction 
has  been  proposed  by  General  Baeyer.*  On  the  ground  that  the  atmos- 
phere, or  at  least  that  portion  of  it  with  which  barometric  calculations 
would  have  to  deal,  derives  its  heat  principally  from  the  earth,  and  only 
to  a  comparatively  small  degree  from  the  direct  rays  of  the  sun,  he  as- 
sumed that  the  rate  of  decrease  of  temperature  in  the  successive  strata 
of  the  atmosphere  would  vary  as  the  square  of  their  distances  from  the 
centre  of  the  earth;  and  he  represented  the  difference  of  temperature  be- 
tween the  upper  and  lower  stations  by  a  series  of  terms  in  which  the 
first  and  second  powers  of  these  distances,  together  with  constant  coeffi- 
cients whose  values  were  to  be  determined  empirically,  were  involved. 
The  determination  of  the  numerical  values  of  these  coefficients  was  to  be 
based  upon  the  effects  of  refraction,  for  in  this  way  the  actual  variations 
in  the  density  of  the  air  column  would  be  taken  into  account,  and  the 
influence  of  possible  local  disturbances  of  temperature  at  the  extreme 
stations  be  avoided.  General  Baeyer's  mathematical  treatment  of  the 
problem  is  elaborate,  but  not  in  all  particulars  satisfactory.  For  alti- 
tudes of  less  than  six  thousand  feet,  he  assumes,  for  reasons  which  are 
not  clearly  stated,  that  certain  terms  in  his  series  may  be  neglected ; 
and  he  finally  adopts  an  expression  which  makes  the  difference  of  tem- 
perature between  two  stations  increase  directly  as  their  difference  of 
altitude,  thus  apparently  abandoning  the  special  hypothesis  which  was 
to  make  his  formula  essentially  different  from  that  of  Laplace.  The 
examination  of  the  conditions  of  the  problem  for  greater  altitudes  he 
seems  not  to  have  entered  upon.  The  principal  temperature  coefficient, 
moreover,  whose  value  was  deduced  from  observations  upon  atmospheric 
refraction,  was  found  not  to  be  strictly  a  constant.  This  is  readily  ex- 

*  Astronomische  Nachrichten,  Band  XLI.  1855,  pp.  305-336  ;  and  Poggendorff 's  Annalen 
der  Physik  und  Chemie,  Band  XCVIII.  1856,  pp.  371  -  396. 


INTRODUCTORY.  21 

plained,  if  we  admit,  as  we  must,  that  the  actual  rate  of  decrease  of 
temperature  with  increase  of  altitude  does  not  in  all  cases  and  under  all 
circumstances  follow  the  same  law.  A  mean  value  for  this  coefficient  is 
employed  in  the  formula  in  order  to  obtain  a  first  approximate  difference  of 
altitude,  which,  in  its  turn,  is  used  to  get  a  special  value  of  the  coeffi- 
cient, which  will  correspond  better  with  the  actual  conditions  of  the 
case  in  hand.  The  results  obtained  in  this  way  differ  in  a  slight  degree 
from  those  given  by  Laplace's  formula;  but,  as  will  appear  further  on, 
they  are  not  free  from  the  irregularities  and  imperfections  previously  re- 
ferred to,  which  it  is  so  desirable  to  explain  or  correct.  The  conclusion 
reached,  after  a  careful  study  of  General  Baeyer's  discussion,  is  that, 
even  if  we  are  willing  to  allow  that  his  hypothesis  rests  on  a  firmer 
theoretical  basis  than  that  of  Laplace,  the  slight  advantages  gained, 
doubtful  at  best,  are  more  than  counterbalanced  by  the  complexity  of 
the  formula  and  the  character  of  the  numerical  operations  required  in 
its  use. 

The  two  principal,  and  possibly  the  only  radical  changes  proposed  in 
the  correction  for  temperature  alone  thus  appear  to  have  yielded  no  val- 
uable results ;  and  the  simpler  hypothesis  of  Laplace  may  well  be  ac- 
cepted as  practically  the  best  in  the  present  state  of  our  knowledge  of 
the  physics  of  the  atmosphere. 

In  Laplace's  formula  the  correction  for  the  effect  of  moisture  is  intro- 
duced by  increasing  the  value  of  the  temperature  correction  by  about 
one  tenth  of  its  whole  amount;  an  increase  which  in  many  cases  will 
correspond  very  well  to  the  actual  hygrometric  condition  of  the  atmos- 
phere, and  which  has  the  additional  advantage  of  shortening  to  some  ex- 
tent the  numerical  computations.  But  no  claim  for  accuracy  can  be 
urged  in  its  favor.  In  fact,  when  the  mean  temperature  of  the  air  col- 
umn between  two  barometric  stations  falls  below  the  freezing-point  of 
water,  this  mode  of  accounting  for  the  effects  of  moisture  actually  intro- 
duces an  error;  for  the  temperature  term  in  this  case  is  subtractive, 
while  the  correction  for  moisture  should  still  be  additive.* 

Bessel,  in  his  "  Bemerkungen  liber  barometrisches  Hohenmessen,"  f  seems 

*  Compare  a  paper  by  Dr.  Apjohn,  in  the  Proceedings  of  the  Eoyal  Irish  Academy,  Vol.  II. 
1844.     p.  564.     This  is  the  earliest  mention  of  this  source  of  error  which  I  have  met  with, 
t  Astronomische  Nachrichten,  Nos.  356,  357  ;  Altona,  1838. 


22  BAROMETRIC   HYPSOMETRY. 

to  have  been  the  first  to  give  the  question  of  a  separate  correction  for 
the  effect  of  moisture  a  thorough  investigation.  His  discussion  of  the 
subject  is  quite  long,  and  the  resulting  formula  considerably  more  com- 
plex than  that  of  Laplace,  though  not  difficult  to  adapt  for  computation 
with  the  aid  of  appropriate  tables.  In  the  employment  of  this  formula 
it  is  necessary  to  know  the  fraction  which  represents  the  humidity  of 
the  air-column  between  the  two  stations,  for  which  in  practice,  in  the 
absence  of  better  data,  the  mean  of  the  humidities  at  the  extreme  sta- 
tions may  be  substituted. 

Formulae  introducing  a  special  vapor  correction  have  also  been  pub- 
lished by  Plantamour,  Williamson,  Bauernfeind,  Eenny,  Eiihlmann,  and 
others.  Plantamour's  formula*  differs  from  that  of  Bessel  principally 
in  the  augmented  value  of  the  numerical  coefficient,  and  was  the  one 
chosen  by  Colonel  "Williamson  for  translation  into  English  measures.  The 
investigations  of  Dr.  Bauernfeind  f  were  going  on  nearly  at  the  same 
time  as  those  of  Plantamour,  and  led  to  nearly  the  same  results,  so  far  as 
the  improvement  of  the  barometric  formula  is  concerned.  Of  the  other 
interesting  and  valuable  meteorological  results  of  his  investigations  it  is 
not  necessary  here  to  speak.  Eenny,  J  who  appears  also  to  have  been 
an  original  investigator  in  this  field,  applied  the  vapor  correction  by 
subtracting  from  the  observed  heights  of  the  mercury  column  the  amounts 
due  to  the  tension  of  the  aqueous  vapor,  avoiding  in  this  way  any  ref- 
erence to  the  relative  humidity.  The  results  obtained,  however,  by  the 
use  of  this  formula  are  practically  identical  with  those  derived  from 
Plantamour's.  Neither  does  Eiihlmann's  formula  §  differ  essentially  from 
the  two  just  mentioned,  but  it  contains,  more  for  the  sake  of  complete- 
ness than  from  any  hope  of  additional  practical  benefit,  a  small  term  in- 
tended to  take  into  account  the  effect  of  the  attractions  of  the  mountain 
masses  themselves. 

Theoretically  the  formulse  of  this  type  must  be  regarded  as   the   most 

*  Memoires  de  la  Societe  de  Physique  et  d'Histoire  naturelle  de  Geneve,  Tom.  XIII.  1852. 
p.  63. 

t  Beobachtungen  und  Untersuclmngen  liber  die  Genauigkeit  barometrischer  Hohenmessungen, 
etc.  Miinchen,  1862. 

J  Transactions  of  the  Royal  Irish  Academy,  Vol.  XXIII.    1859,   pp.  437-448,  and  623  -  668. 

§  Die  barometrischen  Hohenmessungen,  etc.     Leipzig,  1870. 


INTRODUCTORY. 


23 


nearly  perfect,  and  under  favorable  circumstances  they  will  doubtless 
give  results  which  are  a  closer  approximation  to  the  truth,  and  more  in 
accord  with  each  other  than  those  obtained  when  the  temperature  and 
moisture  corrections  are  combined  in  one.  For,  during  the  warm  season, 
when  the  air  is  relatively  dry,  the  combination  of  the  two  corrections  in 
one  increases  a  quantity  which  is  already  too  large,  while  for  the  winter, 
or  wet  season,  the  moisture  correction  is  underestimated,  and  a  quantity 
already  too  small  is  still  further  diminished.  The  principal  difficulty  in 
the  way  of  a  more  general  adoption  of  this  type  of  formula  lies  in  the 
uncertainty  attending  the  observations  which  have  to  be  depended  upon 
in  estimating  the  humidity  of  the  air.  When  the  mean  of  a  long  series 
can  be  used,  it  is  possible  to  approximate  quite  closely  to  the  real  mean 
humidity,  but  the  error  of  any  single  observation  may  well  be  fully  equal 
to  that  introduced  by  combining  into  one  both  the  temperature  and  moist- 
ure corrections.  In  general,  Laplace's  formula  will  give  higher  results 
than  Plantamour's  in  countries  where  the  climate  is  dry,  and  lower 
where  the  climate  is  moist.  The  numerical  values  of  these  differences 
in  two  cases  are  shown  in  the  following  table,  which  is  made  up  from 
Tables  LIII.  and  LIV.  of  Williamson  :  — 


TABLE   SHOWING   THE   EFFECT   OF   A   SEPARATE   CORRECTION   FOR   MOISTURE. 


Jan. 

Feb. 

Mar. 

Apr. 

May. 

June. 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean. 

Ranga 

I. 

21.5 

19.1 

15.7 

11.3 

7.4 

7.3 

5.7 

7.0 

8.6 

11.6 

15.8 

19.8 

12.6 

15.8 

II. 

4.4 

3.0 

1.3 

-2.5 

-4.0 

-6.0 

-7.7 

-3.2 

-6.0 

-2.1 

0.7 

4.2 

-1.5 

12.1 

Case  I.  is  that  of  Geneva  and  St.  Bernard  in  Switzerland,  whose  dif- 
ference of  altitude  is  6791.4  feet.  The  separate  calculation  of  the  vapor 
correction  gives  for  every  month  of  the  year  a  higher  value  than  is 
obtained  when  it  is  combined  with  the  temperature  correction,  showing 
that  for  this  particular  case  Laplace's  arbitrary  increase  of  the  temperature 
term  was  insufficient.  Case  II.  is  that  of  Sacramento  and  Fort  Churchill, 
where  the  difference  of  altitude  amounts  to  about  4,238  feet.  From  April 
to  October  the  atmosphere  is  very  dry,  and  the  true  correction  for  moisture 
is  seen  to  be  less  than  that  involved  in  Laplace's  formula,  though  the 
two  results  from  yearly  means  agree  remarkably  well. 


24 


BAROMETRIC   HYPSOMETRY. 


The  range  of  the  differences  amounts,  in  the  first  case,  to  15.8  feet; 
which  is  sufficient  to  remove  only  about  one-fifth  part  of  the  discrepancy 
between  the  results  obtained  in  summer  and  in  winter,  as  will  be  seen 
from  the  following  table,  whi6h  gives  the  computed  difference  of  altitude 
between  Geneva  and  St.  Bernard  for  each  month  of  the  year,  from  the 
mean  of  observations  continued  through  six  years,  and  their  variations 
from  the  true  difference  determined  by  spirit-level.  The  grand  mean  for 
the  six  years  is  6782.4  feet,  which  is  less  than  the  true  altitude  by  nine 
feet. 

COMPUTED  DIFFERENCE  OF  ALTITUDE  BETWEEN  GENEVA  AND  ST.  BERNARD. 


By  Spirit-Level  6791.4  feet. 

January  

6745.5 
6762.5 
6788.8 
6794.3 
6799.3 
6819.3 

-45.9 
-28.9 
-   2.6 
+   2-9 
+   7.9 
+  27.9 

July  .. 

6820.9 
6807.8 
6784.8 
6757.9 
6759.6 
6747.8 

+  29.5 
+  16.4 
-    6.6 
-33.5 
-31.8 
-43.6 

February  

August  

March  

September  
October  

April  

Mav  .  . 

November  
December  

June  

The  range  of  error  amounts  here  to  75.4  feet,  although  the  computations 
were  made  with  the  aid  of  tables  which  introduce  the  special  moisture 
correction,  and  the  conditions  were  favorable  for  obtaining  the  best  agree- 
ing results. 

The  different  portions  of  the  formula  have  now  been  made  to  pass  in 
review,  and  it  appears  that  no  changes  in  its  form  or  in  the  numerical 
values  of  its  constant  terms  have  been  sufficient  to  overcome  entirely 
the  observed  discrepancies.  The  further  discussion  of  the  problem  will 
be  the  subject  of  the  next  chapter. 


CHAPTER   II. 

DETAILED    ACCOUNT    OF    THE    INVESTIGATION    IN 
CALIFORNIA. 

FROM  the  summary  account  given  in  Chapter  I.  of  the  principal  changes 
which  have  been  proposed  since  the  time  of  Laplace  for  the  sake  of 
increasing  the  accuracy  of  barometric  measurements,  it  will  be  evident  that, 
after  all  the  real  improvements  have  been  incorporated  into  the  formula, 
there  is  still  a  source  of  uncertainty  in  the  results  obtained,  which  requires 
a  further  examination.  It  was  an  investigation  of  this  kind  which  was 
entered  upon  by  the  California  Survey,  the  primary  object  being  to  secure 
a  table  of  corrections  which  could  be  used  for  increasing  or  diminishing 
the  heights  computed  from  observations  taken  under  widely  varying  con- 
ditions, at  different  seasons  of  the  year  and  at  all  hours  of  the  day,  so 
as  to  attain  as  close  an  approximation  to  the  truth  as  possible.  The 
same  table  would  also  serve  to  indicate  the  hour  of  the  day  in  each 
month  of  the  year  at  which  the  nearest  approach  to  truth  would  be 
attained. 

At  the  time  the  investigation  was  begun  it  was  not  known  to  any 
one  connected  with  the  Survey  that  any  similar  tables  had  ever  been 
published,  or  that  the  subject  had  been  approached  from  this  direction; 
and  even  if  the  many  curious  and  instructive  results  which  a  rather  ex- 
tensive examination  of  the  literature  of  hypsometry  since  the  beginning 
of  the  present  century  has  brought  to  light  had  been  known,  the  neces- 
sity for  undertaking  the  California  investigation  would  have  been  in  no 
wise  diminished,  the  climatic  conditions  on  the  slopes  of  the  Sierra  Ne- 
vada differing  in  so  many  respects  from  those  of  Europe  or  Asia.  The 
brief  sketch  of  the  labors  of  others  upon  this  subject  which  will  be  given 
in  Chapter  III.  will  show,  moreover,  that  no  practical  benefit  appears  to 


26  BAROMETRIC   HYPSOMETRY. 

have  been  derived  from  the  tables  published  or  the  suggestions  made. 
There  is  no  reason  to  believe  that  systematic  corrections,  to  eliminate 
the  errors  due  to  the  season  of  the  year  at  which  the  observations  were 
taken,  have  ever  been  applied  to  any  extensive  series  of  barometric  meas- 
urement either  in  this  country  or  in  Europe. 

With  the  single  exception  of  Colonel  Williamson's  work,  to  which 
reference  has  already  been  made,  there  has  been  nothing  of  importance 
published,  which  has  any  direct  bearing  upon  the  special  phases  of  the 
problem,  as  it  presents  itself  upon  the  Pacific  coast  of  the  United  States. 
Had  he  been  able  to  continue  his  investigations,  he  would  doubtless  have 
given  this  portion  of  the  subject  the  same  careful  study,  and  published 
the  results  with  the  same  painstaking  thoroughness,  which  marks  his 
previous  labors.  In  a  certain  sense  the  present  investigation*  may  be 
regarded  as  supplementary  to  his,  but  its  claims  to  originality  and  novelty 
are  beyond  question. 

The  first  requisite  in  the  investigation  was  the  accumulation  of  trust- 
worthy observations,  taken  at  stated  times  and  continued  regularly  for  a 
long  period,  at  points  whose  differences  of  altitude  were  known  from 
careful  surveys  with  the  spirit-level.  A  year's  observations,  at  least,  would 
be  necessary  to  furnish  data  for  estimating  the  effects  of  the  changes  in 
the  atmosphere  with  the  change  of  seasons;  and  a  much  longer  series, 
to  eliminate  the  possible  abnormal  conditions  prevailing  during  any  one 
month.  The  results  of  the  first  year's  observations  were,  on  the  whole, 
satisfactory,  and  fully  justified  the  continuance  of  the  investigation  for  a 
longer  period.  The  second  year's  results  agreed  in  the  main  quite  well 
with  those  of  the  first  year,  although  there  were  unexpectedly  large  vari- 
ations in  certain  months,  and  it  was  decided  to  prepare  a  first  set  of 
tables  at  the  end  of  the  third  year,  which  would  be  available  for  im- 
mediate use  and  until  they  were  superseded  by  more  accurate  tables,  based 
upon  additional  observations.  The  investigation  had  to  be  suspended, 
however,  after  the  third  year,  from  lack  of  funds,  and  the  additional 
observations  have  not  been  taken.  The  instruments  used  were  all  made 
by  James  Green  of  New  York,  and  consisted  of  cistern  barometers,  with 
verniers  reading  to  two  thousandths  of  an  inch,  and  standard  thermome- 
ters, so  graduated  that  it  was  possible  to  estimate  tenths  of  a  Fahrenheit 
degree  with  ease.  There  was  at  each  station  a  pair  of  these  thermome- 


CORRECTIONS  FOR  CALIFORNIA.  27 

ters,  the  bulb  of  one  being  kept  wet  while  the  other  was  dry,  thus 
furnishing  the  data  for  estimating  the  amount  of  moisture  in  the  air. 
They  were  protected  from  the  effects  of  reflected  heat  as  well  as  from  the 
direct  rays  of  the  sun,  and  placed  in  all  cases  several  feet  above  the 
ground,  in  such  positions  that  there  would  always  be  a  free  circulation 
of  air  about  them.  The  barometers  were  compared  with  each  other  and 
with  the  standard  barometer  at  the  Survey  office,  both  at  the  beginning 
of  the  work  and  subsequently  whenever  a  visit  to  the  stations  made  such 
comparisons  possible.  A  record  of  the  index  errors  was  kept  and  the 
proper  corrections  applied  to  all  the  readings  preliminary  to  the  com- 
putations. 

The  points  selected  as  observing  stations  were  Sacramento,  Colfax,  and 
Summit,  on  the  line  of  the  Central  Pacific  Railroad,  the  altitude  of  each 
station  being  known  from  the  railroad  surveys.  Every  possible  assistance 
was  given  by  the  officers  of  the  railroad,  and  at  Colfax  and  Summit  the 
instruments  were  set  up  in  buildings  belonging  to  the  company.  At 
Sacramento  the  observations  were  taken  on  L  Street,  at  the  house  of  Mr. 
A.  A.  Freeman,  an  employee  of  the  railroad  company  as  draughtsman  in 
the  office  of  the  chief  engineer.  At  Sacramento  and  Colfax  the  position 
of  the  instruments  remained  unchanged  during  the  whole  three  years, 
but  at  Summit  one  change  was  made  necessary  before  the  expiration  of 
the  first  half-year  by  the  removal  of  the  company's  office  to  a  more  con- 
venient spot  near  the  hotel.  The  barometer  hung  about  four  feet  higher 
in  its  new  position,  for  which  allowance  was  made  in  the  computations. 

The  observations  at  Sacramento  were  taken  by  Mr.  Freeman,  or  some 
substitute  during  any  temporary  absence,  and  furnish  a  nearly  unbroken 
record  of  the  changes  of  pressure,  temperature,  and  moisture  in  the  atmos- 
phere for  the  three  years.  The  observer  at  Colfax  was  the  station-agent, 
Mr.  J.  P.  Hodgdon,  or  his  assistant,  Mr.  Logner.  The  monthly  returns 
from  Colfax  were  not  quite  so  complete  as  those  from  Sacramento,  and 
at  one  time  the  barometer  was  out  of  order  so  that  no  observations  could 
be  taken  for  five  days.  The  accidental  omissions,  which  averaged  two  a 
month,  were  so  scattered  that  it  was  generally  possible  to  interpolate  a 
suitable  value  within  such  narrow  limits  of  error  that  the  value  of  the 
monthly  means  would  not  be  perceptibly  affected. 

At  Summit  the  number  of  sporadic  omissions  was  smaller  than  at  Col- 


28  BAROMETRIC  HYPSOMETRY. 

fax,  but  breaks  of  a  longer  duration  were,  unfortunately,  more  frequent. 
At  one  time  there  was  an  interruption  of  ten  days,  caused  by  the  break- 
ing of  the  barometer ;  and  at  other  times  there  were  intervals  of  thirteen 
days  and  of  five  days  in  whidh  no  readings  of  the  barometer  were  taken. 
The  observations  at  Summit  also  came  to  an  end  a  month  before  the  close 
of  the  third  year  by  the  death  of  the  observer,  news  of  which  was  not 
received  by  the  director  of  the  Survey  in  time  to  make  arrangements  for 
the  continuance  of  the  work  by  his  successor  at  the  office.  Several  acci- 
dents, moreover,  happened  to  the  thermometers.  During  the  first  winter 
they  were  both  broken,  and  they  could  not  be  replaced  from  New  York 
for  four  months.  For  this  interval  there  were  no  observations  with  the 
wet  bulb,  and  the  place  of  the  dry  bulb  was  supplied  by  a  thermometer 
belonging  to  the  railroad  company.  This  thermometer  was  found  to  give 
results  agreeing  very  closely  with  those  of  Green's  standard  thermometers, 
and  it  was  not  thought  necessary  to  apply  any  correction  to  its  readings. 
During  the  second  winter  the  wet-bulb  thermometer  was  reported  "  broken 
by  the  snow,"  and  there  was  a  consequent  interruption  in  the  psychro- 
metric  observations  until  a  new  thermometer  could  be  sent  from  San 
Francisco.  The  record  of  the  observations  of  the  psychrometer  shows, 
furthermore,  that  good  results  cannot  be  obtained  during  the  cold  weather 
without  extraordinary  care  on  the  part  of  the  observer.  At  Summit  the 
wet-bulb  thermometer,  for  a  large  part  of  each  winter  season,  was  recorded 
as  standing  within  one  or  two  degrees  of  the  freezing-point  of  water, 
though  the  temperature  of  the  air  might  be  as  much  as  twenty  or  thirty 
degrees  lower.  The  only  explanation  of  this  is  that  the  observers  did  not 
watch  for  the  effects  of  the  evaporation  of  the  film  of  ice  which  formed 
about  the  bulb  of  the  thermometer,  but  recorded  the  reading  too  soon 
after  moistening  the  bulb. 

Another  cause  of  the  irregularity  at  Summit  was  the  frequent  change 
of  observer,  which  occurred  whenever  a  change  was  made  by  the  railroad 
company  in  the  agent  in  charge  of  the  station.  Mr.  C.  F.  Gooding  had 
charge  of  the  instruments  at  this  point  for  the  first  four  months,  and 
was  followed  by  Messrs.  Wales,  Potter,  Stewart,  Shearer,  and  Haskins  in 
succession,  all  of  whom  had  to  be  instructed  in  the  methods  of  observing. 
Their  short  terms  of  service  naturally  interfered  with  their  becoming  skilled 
observers.  Nevertheless,  the  work  seems  to  have  been  done  for  the  most 


CORRECTIONS  FOR  CALIFORNIA.  29 

part  conscientiously,  and  the  inevitable  errors  of  observation  may  fairly 
be  considered  as  eliminated  from  the  monthly  means,  excepting  so  far  as 
relates  to  the  wet  bulb  for  the  times  when  the  temperature  was  below 
thirty-two  degrees.  The  Summit  record  for  the  month  of  August,  1873, 
however,  presented  so  many  anomalies  that  it  was  impossible  to  avoid 
the  conclusion  that  the  observations  were  imperfect  or  that  errors  had 
crept  into  the  record  in  copying.  For  this  reason  the  results  of  this 
month's  work  have  been  considered  of  less  value  and  allowed  less  weight 

o 

in  the  final  discussions. 

The  distances  of  the  stations  from  each  other  in  a  straight  line  and 
their  differences  of  altitude  according  to  the  railroad  surveys  are  as 
follows :  — 

Distance.  Difference  of  altitude. 

Sacramento  to  Colfax 45  miles  2,399  feet 

Colfax  to  Summit 36     "  4,590     " 

Sacramento  to  Summit     .        .        .        .        .       77      "  6,989    " 

The  absolute  altitudes  of  the  railroad  stations  at  these  points  are  given 
as  31,  2,425,  and  7,017  feet  respectively,  but  the  difference  of  altitudes 
given  above  takes  into  account  the  actual  position  of  the  barometers, 
above  or  below  the  level  of  the  railroad  track.  The  approximate  latitude 
of  Sacramento  is  38°  35',  of  Colfax  39°  7',  and  of  Summit  39°  20'. 

Sacramento,  though  so  nearly  at  the  level  of  the  sea,  is  shut  off  by  the 
coast  ranges  of  mountains,  except  through  a  narrow  opening  by  which 
the  river  makes  its  way  to  the  ocean,  from  the  sea-breezes  which  are  so 
strong  at  San  Francisco,  and  other  direct  effects  of  the  vicinity  of  large 
bodies  of  water.  As  a  meteorological  station  it  is  an  excellent  representa- 
tive of  the  great  valley  of  California,  which  stretches  from  the  southeast 
to  the  northwest  between  the  coast  ranges  and  the  Sierra  Nevada,  and 
which,  from  the  nature  of  things,  must  be  the  base  of  operations  in  almost 
all  the  surveys  of  the  mountains  on  either  side.  In  all  barometric  work 
in  the  Sierra  or  on  the  eastern  slope  of  the  coast  ranges  much  better 
results  will  be  obtained  if  the  station  barometer  is  kept  in  the  neighbor- 
hood of  Sacramento,  than  would  be  the  case  if  San  Francisco,  or  other 
point  directly  on  the  coast,  were  used  as  a  base,  though  the  absolute 
altitude  of  the  two  points  above  the  sea-level  might  be  the  same.  The 
results  of  an  attempt  to  determine  barometrically  the  difference  of  level 
between  San  Francisco  and  Sacramento,  given  on  page  48,  will  illustrate 


30  BAROMETRIC   HYPSOMETRY. 

in  a  very  marked  manner  the  effect  of  the  differences  of  climate  on  the 
two  sides  of  the  coast  ranges. 

The  town  of  Colfax  lies  on  the  ridge  between  the  valley  of  Bear 
Eiver  and  that  of  the  North  Fork  of  the  American,  which  is  followed  by 
the  railroad  in  its  ascent  of  the  mountains.  It  is  not  shut  in  by  hills 
on  either  side,  nor  so  exposed  as  to  be  swept  by  violent  winds  or 
affected  by  other  local  causes  of  atmospheric  disturbance.  Snow  falls 
only  at  rare  intervals,  and  never  lies  upon  the  ground  for  any  length  of 
time.  Although  over  2,400  feet  above  the  sea-level,  the  mean  temperature 
of  Colfax  from  June  to  January  is  actually  higher  than  that  of  Sacra- 
mento, which  proves  the  station  to  have  been  well  chosen  as  a  means  of 
getting  data  for  the  study  of  the  peculiar  effects  of  the  abnormally  warm 
belt  of  country  which  stretches  along  the  foot-hills  parallel  to  the  general 
trend  of  the  valley. 

At  Summit  the  conditions  are  not  quite  so  favorable.  The  railroad 
station  stands  a  short  distance  below  the  culminating  point  of  Donner 
Pass,  near  the  west  end  of  the  tunnel,  a  third  of  a  mile  in  length, 
by  means  of  which  the  crossing  of  the  ridge  is  effected.  The  enclos- 
ing hills  on  either  side  rise  with  considerable  steepness  for  several 
hundred  feet,  though  not  so  abruptly  as  to  produce  the  effect  of  a  gorge. 
The  prevailing  winds  are  deflected  somewhat  by  the  ridges  which  bound 
the  approaches  to  the  pass,  and  this  may  possibly  have  some  influence 
upon  the  temperature;  how  much  it  is  impossible  to  say.  A  more  serious 
obstacle  in  the  way  of  getting  perfectly  satisfactory  observations  for  tem- 
perature is  presented  by  the  sheds  built  over  the  railroad  track  to  keep 
it  clear  from  snow,  which  accumulates  during  the  winter  to  the  depth 
of  twenty  feet  or  more  at  this  part  of  the  mountains.  The  snow-sheds 
are  extended  so  as  to  include  the  railroad  office  and  the  approach  to  the 
hotel  during  the  worst  of  the  winter,  and  thus  the  thermometers  may 
not  have  been  fairly  exposed  to  the  open  air  all  the  time  the  observa- 
tions were  going  on.  In  making  the  necessary  reductions  and  computa- 
tions, these  sources  of  error  were  kept  in  mind,  and  any  unusual  or 
remarkable  deviations  examined  with  care. 

The  observations  were  taken  three  times  a  day,  —  at  7  A.  M.,  2  P.  M., 
and  9  P.  M.,  the  hours  recommended  for  the  observers  who  collect 
meteorological  data  for  the  Smithsonian  Institution.  From  observations 


CORRECTIONS  FOR  CALIFORNIA.  31 

taken  at  these  three  hours,  it  has  been  found  that  a  very  good  daily 
mean '  can  be  obtained  by  taking  simply  the  mean  of  the  observations, 
and  it  was  not  thought  necessary  to  adopt  any  more  accurate  method  of 
ascertaining  this  mean ;  such,  for  instance,  as  those  recommended  by 
Colonel  Williamson.*  Hourly  observations,  if  they  could  have  been 
obtained,  would  have  given  results  worthy  of  a  higher  degree  of  confi- 
dence, it  is  true,  but,  with  the  limited  means  available  for  the  prosecu- 
tion of  this  work,  it  is  doubtful  if  the  extra  degree  of  refinement 
attained  would  have  justified  the  outlay  of  money  and  time  requisite 
for  the  numerical  reductions  and  computations.  The  observations  were 
sent  at  the  close  of  each  month  to  the  office  of  the  Survey  at  San 
Francisco,  and  the  reductions  were  made  as  rapidly  as  the  nature  of  the 
case  would  permit.  The  barometric  readings  were  first  corrected  for 
temperature,  and  then  increased  or  diminished  by  the  amount  of  the 
index  error,  so  as  to  bring  all  the  data  into  harmony  with  the  same 
unchanging  standard.  No  index  error  was  applied  to  the  readings  of  the 
thermometers.  The  following  tables  show  the  mean  height  of  the 
barometer  and  the  mean  temperature  for  the  different  months  and  hours 
of  the  day  for  the  whole  time  the  observations  were  continued.  The 
work  was  begun  at  Summit  and  Colfax  earlier  than  at  Sacramento,  so 
that  the  means  of  September,  1870,  are  inserted  for  those  two  stations, 
though  the  computed  results  for  September,  1870,  have  not  been  used  in 
the  subsequent  course  of  the  investigation.  The  means  of  the  wet-bulb 
thermometer  have  not  been  included,  partly  because  of  the  incomplete- 
ness of  the  record,  and  partly  because  use  was  not  made  of  them  in  the 
computations.  In  some  cases  the  means  given  were  derived  from  obser- 
vations extending  over  only  a  part  of  a  month,  but  in  only  one  month 
were  observations  lacking  for  more  than  eight  days.  For  July,  1872, 
the  means  for  Summit  are  derived  from  observations  continued  only  from 
the  first  to  the  fifteenth  of  the  month.  The  completeness  of  the  record 
at  Sacramento  usually  served  as  a  guide  in  estimating  how  far  the  results 
derived  from  incomplete  data  could  be  regarded  as  fair  representatives 
of  the  monthly  record,  and  did  away  with  the  necessity  of  giving  any 
further  special  discussion  to  those  cases. 

*  On  the  Use  of  the  Barometer,  p.  158. 


32 


BAROMETRIC  HYPSOMETRY. 


MONTHLY  MEANS  OF  BAROMETER  AND  THERMOMETER 
AT  SACRAMENTO.    (BAROMETER  REDUCED  TO  32°  F.) 


Month  and  Hour. 

BAROMETER. 

THERMOMETER. 

1870. 

1871. 

1S72. 

1373. 

1870. 

1871. 

1872. 

1873. 

January         7  A.M. 

30.173 
30.141 
30.148 
30.154 

30.103 
30.088 
30.083 
30.091 

30.146 
30.140 
30.114 
30.133 

30.016 
29.997 
29.976 
29.996 

29.992 
29.965 
29.962 
29.973 

29.939 
29.914 
29.896 
29.916 

29.914 
29.883 
29.869 
29.889 

29.918 

29.878 
29.861 
29.886 

29.932 

29.897 
29.885 
29.905 

30.032 
29.989 
29.984 
30.001 

30.068 
30.043 
30.046 
30.052 

30.116 
30.090 
30.101 
30.102 

30.029 
30.002 
29.994 
30.008 

30.158 
30.157 
30.166 
30.160 

30.087 
30.071 
30.082 
30.080 

30.111 
30.074 
30.080 
30.088 

30.079 
30.038 
30.049 
30.055 

29.954 
29.910 
29.917 
29.927 

29.943 

29.897 
29.914 
29.918 

29.930 

29.882 
29.880 
29.897 

29.911 
29.864 
29.863 
29.879 

29.944 
29.905 
29.916 
29.921 

30.022 
29.973 
29.984 
29.993 

30.165 
30.110 
30.133 
30.136 

30.071 
30.056 
30.070 
30.066 

30.031 
29.995 
30.004 
30.010 

30.152 
30.131 
30.135 
30.139 

30.076 
30.054 
30.065 
30.065 

30.143 
30.118 
30.125 
30.129 

30.106 
30.085 
30.113 
30.101 

29.920 
29.901 
29.898 
29.906 

29.971 
29.961 
29.957 
29.963 

29.909 
29.871 
29.894 
29.8S1 

29.987 
29.943 
29.967 
29.966 

29.932 

29.874 
29.915 
29.907 

49.3 
72.6 
57.3 

59.8 

42.0 
62.9 
50.1 
51.7 

34.7 
50.6 
41.9 
42.4 

38.1 
52.8 
44.7 
45.2 

39.4 
54.1 
47.3 
46.9 

45.5 
62.4 
54.6 
54.2 

49.3 
67.3 

56.8 
57.8 

53.6 
71.2 
59.5 
61.4 

61.9 
84.1 

68.6 
71.5 

60.3 
85.0 
68.3 
71.2 

CO.  8 
89.6 
69.8 
73.4 

55.2 
79.9 
65.2 
66.8 

49.7 
74.0 
58.6 
60.8 

42.0 
60.1 
47.5 
49.9 

42.9 
50.3 
45.7 
46.3 

49.9 
69.2 
57.2 
58.8 

42.0 
49.2 
45.4 
45.5 

47.6 
55.5 
50.8 
51.3 

48.0 
60.3 
53.2 
53.8 

51.8 
64.6 
56.6 
57.7 

62.4 
76.2 
62.4 
67.0 

64.5 

78.0 
65.2 
69.2 

66.0 

82.2 
68.2 
72.1 

63.5 
82.0 
67.6 
71.0 

59.4 
77.7 
64.5 
67.2 

51.5 
72.2 
56.9 
60.0 

43.6 

60.8 
47.8 
50.7 

42.2 
54.5 
45.6 
47.4 

53.5 
67.8 
57.0 
59.4 

44.8 
57.6 
49.7 
50.7 

41.9 
54.6 

47.8 
48.1 

48.9 
65.8 
54.8 
56.5 

58.6 
70.3 
57.9 
62.3 

63.3 
76.5 
64.5 
68.1 

67.7 
80.7 
67.4 
71.9 

70.2 
86.7 
76.4 

77.8 

63.0 
81.6 
63.6 
69.4 

60.1 
81.9 
62.8 
68.3 

2  P.M. 
9  P.M. 

MEAN 
February       7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
March           7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
April             7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
May               7  A.  M. 

2  P.M. 
9  P.M. 

MEAN 
June              7  A.M. 

2  P.M. 

9  P.M. 

MEAN 

July              7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
August          7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
September     7  A.M. 

2  P.M. 
9  P.M 

MEAN 
October         7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
November     7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
December      7  A.M. 

2  P.M. 
9  P.M. 

MEAN 

MEAN  OF    7  A.M. 
YEAR         2  P.M. 

9  P.M. 

GRAND  MEAN  

29.980 
29.949 
29.949 
29.959 

30.131 
30.093 
30.106 
30.110 

30.179 
30.142 
30.152 
30.158 

CORRECTIONS  FOR  CALIFORNIA. 


33 


MONTHLY  MEANS  OF  BAROMETER  AND  THERMOMETER 
AT   COLFAX.     (BAROMETER  REDUCED  TO  32°  F.) 


Month  and  Hour. 

BAROMETER. 

THERMOMETER. 

1870. 

1871. 

1872. 

1873. 

1870. 

1871. 

1872. 

1873. 

January         7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
February       7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
March           7  A.M. 

2  P.  M. 
9  P.M. 

MEAN 
April             7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
May               7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
June              7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
July               7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
August          7  A.M. 

27.632 
27.607 
27.627 
27.622 

27.543 
27.540 
27.524 
27.536 

27.599 
27.603 
27.595 
27.599 

27.507 
27.496 
27.492 
27.498 

27.479 
27.473 
27.471 
27.475 

27.494 
27.484 
27.493 
27.490 

27.468 
27.470 
27.465 

27.468 

27.492 
27.486 
27.486 
27.488 

27.482 
27.464 

27.478 
27.475 

27.564 
27.527 
27.545 
27.545 

27.548 
27.528 
27.540 
27.539 

27.576 

27.55(3 
27.533 
27.562 

27.532 
27.520 
27.52'2 
27.525 

27.608 
27.607 
27.616 
27.610 

27.555 
27.547 
27.563 
27.555 

27.564 
27.554 
27.569 
27.562 

27.523 
27.524 
27.535 

27.527 

27.470 
27.466 
27.472 
27.469 

27.486 
27.493 
27.497 
27.492 

27.473 

27.468 
27.476 
27.472 

27.479 
27.470 
27.476 
27.475 

27.518 
27.507 
27.511 
27.512 

27.569 
27.548 
27.571 
27.563 

27.627 
27.605 
27.635 
27.622 

27.555 
27.535 
27.560 
27.550 

27.536 
27.527 
27.540 
27.534 

27.634 

27.595 
27.629 
27.619 

27.510 

27.505 
27.516 
27.510 

27.614 
27.593 
27.618 
27.608 

27.553 
27.536 
27.552 
27.547 

27.418 
27.423 
27.427 
27.423 

27.486 
27.472 
27.493 
27.484 

27.467 
27.476 
27.486 
27.476 

27.494 
27.488 
27.504 
27.495 

27.486 
27.4(50 
27.482 
27.476 

-vd_ 

61.9 
81.8 
65.2 
69.6 

53.2 
73.0 
57.8 
61.3 

46.5 
62.1 
50.5 
53.0 

37.4 
51.6 
41.4 
43.5 

40.9 
55.9 
44.9 
47.2 

37.6 
50.2 
42.3 
43.4 

44.1 

56.8 
47.7 
49.5 

49.7 
63.2 
50.5 
54.5 

56.0 
69.0 
54.9 
60.0 

70.0 
86.7 
69.8 
75.5 

72.8 
90.7 
73.7 
-79.0 

73.9 
94.4 
75.7 
81.3 

61.6 
84.3 
65.5 
70.5 

56.0 
76.9 
59.1 
64.0 

44.5 
58.3 
48.1 
50.3 

44.8 
55.1 
48.4 
49.4 

54.3 
70.1 
56.7 
60.4 

40.4 
53.8 
43.9 
46.1 

43.9 
53.2 
47.3 
48.1 

45.7 
58.9 
49.1 
51.3 

46.9 
59.8 
49.7 
52.1 

62.7 
76.4 
62.7 
67.3 

66.5 
82.4 
67.9 
72.3 

72.9 
89.7 
73.7 

78.8 

71.5 
91.5 
70.6 
77.9 

64.4 

82.0 
65.3 
70.5 

57.0 

76.2 
59.7 
64.3 

46.9 
61.6 
49.5 
52.7 

43.4 
56.6 
46.2 

48.7 

55.2 
70.2 
57.1 
60.8 

45.9 

57.9 
49.2 
51.0 

37.0 

47.4 
39.9 
41.4 

48.0 
63.5 
50.4 
54.0 

50.4 
64.3 
52.4 

55.7 

59.3 
74.0 
60.2 
64.5 

67.6 

83.5 
65.8 
72.3 

75.9 
93.3 
75.4 
81.5 

70.2 

88.8 
69.6 
76.2 

65.5 

85.8 
68.4 
73.2 

2  P.M. 
9  P.M. 

MEAN 
September     7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
October          7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
November     7  A.M. 

2  P.M. 
9  P.M. 

MEAN 

December      7  A.M. 

2   P.M. 
9  P.M. 

MEAN 

MEAN  OF    7  A.M. 
YEAR         2  P.M. 

9  P.M. 

GRVND  MFAN 

27.4S2 
27.463 
27.475 
27.473 

27.511 

27.491 
27.502 
27.502 

27.618 
27.594 
27.611 
27.607 

27.614 

27.581 
27.602 
27.599 

34 


BAROMETRIC  HYPSOMETRY. 


MONTHLY  MEANS   OF  BAROMETER   AND   THERMOMETER 
AT  SUMMIT.    (BAROMETER  REDUCED  TO  32°  F.) 


Month,  and  Hour. 

BAROMETER. 

THERMOMETER. 

1870. 

1871. 

187^ 

1873. 

1870. 

1871. 

1872. 

1873. 

January         7  A.M. 

23.302 
23.289 
23.300 
23.297 

23.170 
23.165 
23.172 
23.169 

23.247 
23.259 
23.256 
23.254 

23.194 
23.195 
23.204 
23.198 

23.227 
23.230 
23.235 
23.231 

23.350 
23.360 
23.362 
23.357 

23.368 
23.367 
23.364 
23.366 

23.413 
23.403 
23.411 
23.409 

23.343 
23.331 
23.343 
23.339 

23.383 
23.358 
23.369 
23.370 

23.233 
23.211 
23.223 
23.222 

23.240 
23.214 
23.226 
23.227 

23.289 
23.282 
23.289 
23.287 

23.267 
23.253 
23.276 
23.265 

23.180 
23.187 
23.190 
23.186 

23.226 
23.225 
23.232 
23.228 

23.182 
23.192 
23.205 
23.193 

23.265 
23.265 
23.264 
23.265 

23.324 
23.321 
23.330 
23.325 

23.361 
23.346 
23.363 
23.356 

23.341 
23.324 
23.343 
23.336 

23.347 
23.336 
23.346 
23.343 

23.365 
23.337 
23.354 
23.352 

23.366 
23.325 
23.351 
23.347 

23.258 
23.245 
23.267 
23.257 

23.290 
23.280 
23.293 
23.288 

23.310 
23.285 
23.307 
23.301 

23.102 
23.095 
23.117 
23.105 

23.308 
23.292 
23.314 
23.305 

23.254 
23.255 
23.259 
23.256 

23.201 
23.190 
23.217 
23.203 

23.325 
23.305 
23.323 
23.318 

23.390 
23.393 
23.397 
23.393 

23.326 
23.323 
23.324 
23.324 

50.4 
64.9 
45.5 
53.6 

38.7 
53.4 
40.8 
44.4 

29.7 
43.4 
32.1 
35.1 

18.9 
31.9 
22.6 
24.5 

22.8 
34.3 
25.0 

27.4 

19.8 
30.7 
23.5 
24.6 

24.9 
36.0 
24.6 
28.5 

33.2 
42.6 
28.0 
34.6 

43.3 

51.2 
35.3 
43.3 

57.8 
70.1 
51.1 
59.7 

56.7 
71.1 
53.1 
60.3 

57.3 
76.1 
53.4 
62.3 

52.0 
65.4 
45.2 
54.2 

39.8 
61.8 
39.9 
47.2 

27.1 
38.6 
28.6 
31.4 

27.5 
35.1 
30.1 
30.9 

38.5 
51.1 
36.5 
42.0 

24.9 
31.0 
27.8 
27.9 

29.0 
32.0 
30.4 
30.5 

28.8 
34.5 
31.1 
31.5 

27.2 
33.6 

28.5 
29.8 

40.3 
49.5 
40.4 
43.4 

51.1 
60.2 
46.1 
52.5 

55.4 
65.5 
54.3 
58.4 

51.6 
66.7 
52.5 
56.9 

46.3 
62.5 
49.9 
52.9 

41.6 
56.5 
43.4 
47.2 

32.0 
44.7 
32.3 
36.3 

27.2 
38.0 
30.4 
31.8 

38.0 
47.9 
38.9 
41.6 

28.8 
37.3 
30.7 
32.3 

24.6 
30.0 

25.8 
26.8 

30.3 

40.8 
33.3 
34.8 

32.8 
43.4 
34.7 
37.0 

39.0 
53.8 
42.1 
45.0 

47.0 
59.9 
51.0 
52.6 

61.6 
69.0 
62.2 
64.3 

53.9 
62.7 
57.7 
58.1 

; 

2  P.M. 
9  P.M. 

MEAN 
February        7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
March           7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
April             7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
May              7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
June              7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
July              7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
August          7  A.M. 

2  P.M. 
9  P.  M. 

MEAN 
September     7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
October         7  A.M. 

2  P.M. 
9  P.M. 

MEAN 
November     7  A.M. 

2  P.M. 
9P.M. 

MEAN 

December      7  A.M. 

2  P.M. 
9  P.M. 

MEAN 

MEAN  OF    7  A.M. 
YEAR         2  P.M. 

9  P.M. 

GRAND  MEAN  

23.334 
23.326 
23.335 
23.332 

23.331 
23.323 
23.335 
23.329 

23.359 
23.339 
23.358 
23.352 

23.284 
23.261 
23.277 
23.274 

CORRECTIONS  FOR  CALIFORNIA.  35 

From  what  has  been  said  about  the  observations  of  the  wet-bulb 
thermometer,  taken  in  connection  with  the  fact  that  one  of  the  chief 
objects  of  the  investigation  was  to  prepare  a  table  of  corrections  to  be 
applied  to  results  obtained  in  different  years  and  without  reference  to 
the  element  of  moisture,  it  is  evident  that  for  purposes  of  computation 
the  choice  lay  between  the  tables  of  Guyot  and  those  of  Williamson, 
with  omission  of  the  portions  relating  especially  to  the  effect  of  the 
vapor  in  the  atmosphere.  The  observations  of  the  first  year,  from  Octo- 
ber, 1870,  to  September,  1871,  were  computed  by  both  sets  of  tables, 
and  the  decision  reached  that  Williamson's  tables,  which  make  altitudes 
about  four  feet  in  a  thousand  higher  than  those  of  Guyot,  give  results 
which,  when  the  means  of  a  long  series  are  used,  accord  best  with  the 
true  differences  of  altitude  determined  by  the  spirit-level.  With  Guyot's 
tables  the  errors  of  midday  observations,  it  is  true,  are  reduced,  but  those 
of  morning  and  evening  are  correspondingly  increased.  The  computa- 
tions for  Tables  I. -IX.,  which  form  the  basis  of  the  subsequent  tables 
of  corrections,  were  all  made  with  aid  of  Williamson's  tables,  the  cor- 
rection for  temperature  in  all  cases  being  made  by  multiplying  the  first 
approximate  difference  of  altitude  by  the  sum  of  the  temperatures  of  the 
air  at  the  two  stations  diminished  by  64,  and  then  dividing  by  900. 
The  corrections  for  latitude  and  for  decrease  of  gravity  were  applied 
separately  in  each  computation. 

Tables  I. -III.  give  the  difference  of  altitude  between  Sacramento  and 
Colfax,  determined  barometrically  from  the  mean  of  the  7  A.  M.,  the  2 
p.  M.,  and  the  9  P.  M.  observations  as  well  as  from  the  mean  of  the  day 
for  each  month,  and  from  the  mean  of  the  year,  for  the  three  years  from 
October,  1870,  to  September,  1873.  The  difference  between  the  baro- 
metric determinations  and  the  true  difference  of  altitude  is  also  shown  in 
the  parallel  columns.  Tables  IV. -VI.  and  VII. -IX.  comprise  the  same 
data  for  the  stations  Sacramento  and  Summit,  and  Colfax  and  Summit 
respectively.  Tables  X. -XII.,  which  show  the  means  of  these  years, 
were  deduced  from  the  preceding  tables,  and  not  computed  indepen- 
dently from  the  means  of  the  recorded  observations,  as  it  was  found  from 
a  few  trials  that  the  results  would  be  practically  identical. 

An  inspection  of  these  twelve  tables  leads  unmistakably  to  the  follow- 
ing conclusions. 


36  BAROMETRIC   HYPSOMETRY. 

I.  Tlic  results   are   always  louvr   at   morning   and   night   than   at   mid- 
day.    To  this  statement  there  is  absolutely  no  exception. 

II.  The  results   are   lower   in   winter  than  in  summer.     This  must  also 
be  regarded  as  universally  true,  in  spite  of  certain  anomalies,  for  which 
no   complete   explanation   suggests   itself.     For  instance,  in  Tables  I.  and 
IV.,  it  appears   that  the  9  p.  M.  result  was  actually  higher  in  February, 
1871,  than  in  June,  July,  or  August  of  that  year,  when  the  computations 
were  made  with  reference  to  Sacramento  as  the  lower  station,  though  the 

'  O 

anomaly  is  less  strongly  marked  in  Table  VII.  for  which  the  lower 
station  was  Colfax.  In  Table  II.  the  9  P.  M.  result  for  December  was 
the  highest  of  the  evening  results,  with  one  exception,  for  the  whole  of 
the  second  year;  while  Tables  V.  and  VIII.,  which  cover  the  same  time  as 
Table  II.,  show  the  maximum  evening  result  of  the  whole  year  in 
February. 

The  only  explanation  that  can  be  offered  is,  that,  in  February  and  De- 
cember, 1871,  there  were  unusual  conditions  of  the  atmosphere  prevailing 
in  the  valley,  and,  in  February,  1872,  upon  the  mountains.  The  expla- 
nation is  far  from  satisfactory,  but  it  seems  impossible  to  regard  the 
anomalies  as  due  to  imperfections  in  the  observations.  There  is  no 
reason  to  believe  that  the  observers  made  any  change  in  the  positions 
of  the  instruments  or  exercised  less  than  their  ordinary  care  in  observ- 
ing during  those  months. 

Abnormally  high  results  for  both  morning  and  evening  appear  also  in 
Tables  VI.  and  IX.,  for  the  month  of  February,  1873.  The  absence  of 
corresponding  irregularities  in  Table  III.  points  again  to  the  mountains 
as  the  seat  of  the  disturbance.  In  fact,  the  barometer  at  Summit  stood 
lower  for  the  month  of  February,  1873,  than  for  any  other  month  during 
the  whole  three  years ;  while,  both  at  Sacramento  and  Colfax,  the  barom- 
eter, though  lower  than  for  the  same  month  in  the  preceding  years,  was 
by  no  means  at  its  minimum. 

III.  From  the  two  preceding  considerations  it  follows  that,  as  a  general 
rule,   the   lower   the   temperature   of  the   locality,   the   lower   the   barometric 
result,  and  vice  versa. 

IV.  Altitudes  determined  from  daily  means  approximate   most   closely  to 
the  truth  in  February,  September,  and  October  between  Sacramento  and 
Colfax;  that  is  to  say,  during  the  months  of  transition  from  one  extreme 


CORRECTIONS  FOR  CALIFORNIA.  37 

season  to  the  other.  Between  Sacramento  and  Summit  the  best  results 
from  daily  means  are  obtained  in  the  summer  months,  from  June  to 
August ;  while  between  Colfax  and  Summit  the  best  daily  means  are  to 
be  expected  in  March,  April,  and  September. 

V.  The  mean   of  the  day  for  points  in  the  foot-hills   is  much  too  high 
during  the  summer,  though   not  far  from  the   truth   in   the  winter;    but 
for  mountain  localities,  the  station  barometer  being  kept  in  the  valley  in 
both  cases,  the  summer  season  gives  the  best  approximation,  the  results 
in  winter  being  much  too  low. 

VI.  Midday  observations  give  results  which  are  greatly  too  high  all   the 
year  round  in  the  valley  and  foot-hills.     The  excess  sometimes  amounts  in 
summer  to  more  than  a  hundred   feet,  and  seldom,  if  ever,  falls  below 
twenty-five   feet,  between   Sacramento   and  Colfax,  whose  true   difference 
of  altitude  is  only  twenty-four  hundred  feet.     Between  Sacramento  and 
Summit  the  results  from  the  2  P.  M.  observations  were  always  too  high 
except  in  the  months  of  December  or  January,  and  the  excess  in  one 
instance  amounted  to  over  one  hundred  and  ninety  feet.     Only  once  did 
the  result   of  the   two -o'clock   observation  fall  too   low  between  Colfax 
and  Summit,  and  then  by  only  six  feet. 

VII.  TJie  7  A.  M.  and  9  P.  M.  observations  give  results  which  agree,  in  the 
main,  with  each  other.     Both  hours  give  results  too  low  all  the  year  round, 
almost  without  exception,  between  Sacramento  and  Summit  and  between 
Colfax  and  Summit.     In  the  foot-hills  the  morning  and  evening  results 
are  generally  too  high  in  summer  and  too  low  in  winter,  but  the  separate 
years  do  not  show  this  so  clearly  as  the  mean  of  the  three  years.     In  the 
case  of  the  7  A.  M.  observations  the  discrepancy  between  barometric  meas- 
urements and  the  truth  was  enormous  in  winter,  amounting  in  one  in- 
stance  to   two   hundred    and   thirty-eight   feet    between   Sacramento   and 
Summit,  or  about  three  and  one  half  per  cent  of  the  total  difference  of 
altitude. 

VIII.  The  mean   of  the   year  is  a  little    too   high  between   Sacramento 
and  Colfax,  too  low  between  Sacramento  and  Summit,  and  quite  near  the 
truth  between  Colfax  and  Summit.     The  following  suggestion  is  offered  as 
possibly  furnishing  the  key  to  the  explanation  of  this  fact.     Owing  to  the 
necessary  position   of  the   thermometers   within   only  a  few   feet   of  the 
ground,  the  mean  temperature  of  the  air  for  the  year  at  Summit  is  prob- 


38  BAROMETRIC   HYPSOMETRY. 

ably  estimated  a  little  too  low,  the  lowest  stratum  of  air  being  cooled  by 
the  presence  and  evaporation  of  the  snow.  At  Colfax,  on  the  other  hand, 
where  no  snow  falls,  and  where  the  surface  of  the  earth  is  intensely 
heated  in  summer,  the  result  would  naturally  be  the  other  way.  If  these 
two  errors  balanced  each  other  exactly,  an  accurate  result  might  be  ex- 
pected from  the  yearly  means  at  Colfax  and  Summit,  while  the  observed 
discrepancies  would  show  themselves  when  these  two  stations  were  com- 
pared respectively  with  Sacramento. 

Tables  XIII. -XVI.  were  prepared  from  the  data  contained  in  the 
preceding  tables  for  the  sake  of  showing  the  effect  of  introducing  an 
intermediate  station,  part  way  up  the  slope,  upon  the  calculated  differences 
of  altitude  between  the  valley  and  points  high  up  on  the  Sierra.  These 
tables  need  no  detailed  explanation.  The  prominent  fact  brought  to  view- 
is  that  the  use  of  Colfax  as  an  intermediate  station  increases  the  calculated 
difference  of  altitude  between  Sacramento  and  Summit  at  all  seasons  of 
the  year  and  at  all  hours  of  the  day.  For  more  than  two  thirds  of  the 
time  this  increase  lies  between  thirty  and  seventy  feet,  and  may  thus  be 
regarded  as  tolerably  constant.  The  effect  of  this  is  to  change  the  times 
at  which  the  nearest  approximations  to  the  truth  are  to  be  expected;  to 
increase  the  error,  when  the  direct  measurements  are  already  too  high ;  and 
to  diminish  it  in  cases  of  the  opposite  character.  The  same  tables  also 
show  incidentally  the  abnormal  character  of  the  results  in  February,  1873, 
and,  to  a  less  degree,  of  those  in  February,  1872,  and  April,  1873.  The 
minus  sign  in  the  column  of  differences  for  2  P.  M.,  Table  XV.,  is  an  addi- 
tional proof  of  the  partial  untrustworthiness  of  the  Summit  record  of 
August,  1873,  and  justification  of  the  decision  to  assign  a  less  weight  than 
usual  to  that  month's  results. 

In  Tables  XVII.  -  XIX.,  which  present  a  comparative  view  of  the  results 
for  three  years,  columns  headed  "  range "  have  been  added  in  order  to 
show  at  a  glance  how  measurements  made  at  the  same  season  in  different 
years  vary  from  each  other.  For  Sacramento  and  Colfax,  Table  XVII.,  the 
range  averages  less  in  the  winter,  from  September  to  March,  than  in  sum- 
mer; but  for  Colfax  and  Summit,  Table  XIX.,  the  agreement  is,  on  the 
whole,  much  better  in  summer  than  in  winter.  The  changes  from  mouth 
to  month  also  are,  at  these  seasons,  least  erratic.  The  great  heat  of  the 
summer  upon  the  foot-hills  seems  to  have  a  greater  disturbing  influence 


CORRECTIONS  FOR  CALIFORNIA.  39 

than  the  rains  of  winter;  while,  when  mountain  stations  alone  are  con- 
sidered, the  atmosphere  in  summer  is  much  more  uniform  from  year  to 
year  than  it  is  in  winter.  On  Table  XVIII.,  Sacramento  and  Summit, 
the  range  is  both  larger  in  amount  and  more  unevenly  distributed  than 
on  either  of  the  other  two  tables,  which  might  be  reasonably  expected  from 
the  positions  of  the  stations.  In  some  cases  the  large  variations  in  suc- 
cessive years  arise  from  obviously  anomalous  conditions,  the  nature  of  which, 
however,  it  is  not  easy  to  point  out ;  and  the  practical  conclusion  to  be 
drawn  is,  that  the  longer  the  observations  are  continued  and  the  more 
frequently  they  are  taken  each  day,  the  freer  the  final  mean  will  be  from 
serious  errors. 

When  the  data  of  these  tables  are  represented  graphically  by  curves,  it 
is  more  clearly  evident  than  it  can  be  from  an  inspection  of  the  figures 
alone,  that  a  period  of  three  years  even  is  not  long  enough,  if  observations 
are  taken  only  three  times  a  day,  to  eliminate  all  the  irregularities  inci- 
dent to  the  use  of  the  barometer  in  the  Sierra;  and  that  a  much  better 
mean  curve  and  a  much  more  probable  table  of  errors  will  be  obtained 
if  the  most  strikingly  obvious  discrepancies  are  not  allowed  to  enter  with 
full  force  into  the  mean  values.  Tables  XX.  -  XXII.  are  mean  tables  so 
made  as  to  represent  as  nearly  as  possible  the  most  probable  mean  values 
of  the  errors  at  different  seasons  and  different  hours  of  the  day. 

Table  XX.  was  constructed  in  the  following  manner.  A  horizontal  line 
was  assumed  to  represent  the  true  difference  of  altitude  between  Sacra- 
mento and  Colfax,  and  at  equal  intervals  along  this  line  perpendicular 
distances  were  laid  off  to  represent  the  error  of  the  7  A.  M.  observations 
for  each  month  of  each  year.  The  horizontal  and  vertical  scales  were  so 
chosen  that  the  curves,  which  resulted  from  joining  corresponding  points, 
showed  very  clearly  any  deviation  from  regularity.  The  three  curves, 
thus  plotted  upon  the  same  sheet  of  paper,  by  no  means  coincided, 
though  the  general  features  presented  by  each  were  the  same.  The 
curve  for  the  mean  of  three  years  was  not  plotted.  The  mean  curve 
adopted  was  a  more  regular  one,  drawn  with  a  free  hand  in  such  a  way 
as  to  neutralize,  as  far  as  possible,  all  abnormal  irregularities.  The 
proper  perpendicular  distances  of  this  curve  from  the  horizontal  line 
were  then  carefully  measured  on  the  paper,  and  the  amounts  entered  in 
the  table  as  the  approximate  error  of  barometric  measurements  for  7  A.  M. 


40  BAROMETRIC  HYPSOMETRY. 

The  same  course  was  taken  with  the  other  hours  and  the  mean  of  the 
day;  and  similarly  for  Tables  XXI.  and  XXII.  Constructed  in  this  way, 
these  tables  are  believed  to  give  the  best  approximation  to  the  truth 
attainable  from  the  given  observations.  They  show,  moreover,  in  some 
particulars,  more  clearly  than  the  first  twelve  tables,  the  grounds  for  the 
conclusions  which  have  been  given  above. 

To  give  to  the  investigation  the  greatest  practical  value,  it  was  neces- 
sary, furthermore,  to  prepare  a  table  of  corrections,  which  could  be  used 
for  observations  taken  at  different  hours  of  the  day,  and  at  other  points 
than  those  specially  considered  in  the  discussion,  but  where  the  atmos- 
pheric conditions  might  fairly  be  supposed  analogous. 

Tables  XXIII. -XXV.  are  of  this  kind,  and  give  the  correction,  to  be 
added  or  subtracted,  for  each  thousand  feet  of  difference  of  altitude  at 
different  hours  in  the  several  months.  The  numbers  in  heavy-faced  type 
were  obtained  directly  from  Tables  XX. -XXII.  by  division,  and  thus 
rest  upon  the  foundation  of  actual  observations.  The  remaining  numbers 
were  obtained  by  the  following  method  of  interpolation.  The  corrections 
for  each  month  were  laid  down  upon  paper  in  a  manner  similar  to  that 
previously  described  and  the  three  points  joined  by  a  curved  line;  the 
season  of  the  year,  the  times  of  sunrise  and  sunset,  and  the  probable 
rate  of  change  in  the  value  of  the  correction  from  morning  to  noon  and 
from  noon  to  night,  being  all  taken  into  account.  The  change  in  the 
correction,  for  instance,  was  assumed  to  be  most  rapid  during  the  hours 
that  the  temperature  of  the  air  was  changing  most  rapidly,  and  to  be 
comparatively  slight  for  the  two  or  three  hours  near  the  hottest  part  of 
the  day,  and  for  the  hours  after  sunset.  No  attempt  was  made  to  sup- 
ply corrections  for  the  night  hours,  the  data  not  being  sufficient  for  the 
purpose,  and  there  being  no  practical  use  to  be  made  of  them. 

The  most  striking  fact  brought  out  by  a  comparison  of  these  three 
tables  with  each  other  is  a  remarkable  difference  in  the  value  of  the 
correction  for  each  thousand  feet,  depending  upon  the  position  of  the 
stations.  For  three  o'clock  in  the  afternoon  of  June,  the  minus  correc- 
tion amounts  to  36.5  feet  in  a  thousand  for  the  foot-hills,  and  to  only 

i 

21.6  feet,  if  the  upper  station  is  high  in  the  mountains,  —  a  difference  of 
14.9  feet.  The  difference  is  even  greater  in  the  month  of  December, 
amounting  for  10  A.  M.  to  19.4  feet.  The  corrections  for  the  early  morn- 


CORRECTIONS  FOR  CALIFORNIA.  41 

ing  hours  also,  in  Tables  XXIV.  and  XXV.,  are  positive  the  year  round, 
while  in  Table  XXIII.  they  are  negative  from  April  to  September.  A 
partial  explanation  of  these  results  is  to  be  found  in  the  fact  that  the 
temperature  of  the  air  in  California  does  not  decrease  regularly  from  the 
sea-level  to  the  summit  of  the  mountains,  as  it  is  supposed  to  do  in 
the  development  of  the  barometric  formula.  In  the  summer  especially 
the  stratum  of  maximum  temperature  lies  at  an  altitude  of  several  hun- 
dred feet  above  the  valley,  though  probably  not  so  high  as  Colfax. 

After  this  description  of  the  tables,  it  only  remains  to  point  out  the 
ways  in  which  they  are  expected  to  contribute  to  the  accuracy  of  baro- 
metric work  in  California,  the  problem  being  to  make  as  close  an  ap- 
proximation as  possible  to  the  real  difference  of  altitude  from  a  single 
observation  or  the  mean  of  a  short  series. 

If  the  observer  has  it  in  his  power  to  fix  the  time  of  day  at  which 
his  observation  shall  be  made,  or  to  extend  his  observations  over  the 
whole  day,  it  is  easy  to  see  from  the  tables  how  he  should  be  guided  in 
the  selection  of  his  hours.  Or,  if  the  observer  is  obliged  to  take  his 
observation  at  a  certain  fixed  hour,  the  tables  will  supply  the  correc- 
tion, corresponding  to  the  hour  of  the  day  and  the  season  of  the  year, 
which  will  bring  the  computed  result  into  closer  agreement  with  the 
truth. 

If  the  points  whose  altitudes  are  to  be  ascertained  are  in  the  foot- 
hills, and  not  more  than  three  thousand  feet  high,  the  station  barometer 
being  observed  in  the  valley  at  some  place  not  much  above  the  sea- 
level,  Table  XXIII.  will  be  the  one  to  use ;  and  the  best  hours  for 
observing  in  the  different  months  will  be  seen  at  once  by  inspection. 
In  January,  for  instance,  the  closest  approximation  to  the  truth  is  at- 
tained between  nine  and  ten  in  the  morning,  or  from  five  to  seven  in 
the  evening.  In  the  month  of  July  nine  in  the  evening  is  the  only 
hour  which  gives  results  requiring  little  or  no  correction ;  but  in  October 
the  middle  of  the  forenoon  and  the  hours  about  sunset  give  equally  good 
results. 

A  similar  use  can  be  made  of  Table  XXIV.  for  those  cases  where  the 
station  barometer  is  kept  in  the  valley  and  the  points  whose  altitudes 
are  desired  lie  between  five  and  eight  thousand  feet  high.  These  limits 
are  mentioned,  not  because  they  have  been  determined  with  accuracy, 


42  BAROMETRIC  HYPSOMETRY. 

but  because  there  is  every  reason  to  believe  that  the  corrections  would 
have  different  values  if  tables  similar  to  these  now  published  could  be 
prepared  for  the  higher  altitudes  and  for  some  station  intermediate  be- 
tween Colfax  and  Summit.  In  the  measurements  of  the  higher  mountain- 
peaks  it  will  generally  be  possible  to  establish  a  camp  or  base  of  reference 
at  some  point  within  the  limits  to  which  the  published  tables  apply,  and 
whose  absolute  altitude  can  be  determined  from  the  mean  of  observa- 
tions taken  under  the  most  favorable  conditions,  or  by  the  use  of  the 
tabular  corrections.  For  the  higher  points,  then,  the  principal  sources  of 
error  would  be  confined  to  that  portion  of  the  distance  which  lies  above 
the  camp  or  temporary  station;  and,  in  the  absence  of  appropriate  tables, 
the  chief  dependence  must  be  placed  upon  the  discretion  and  good  judg- 
ment of  the  observer  in  selecting  his  times  for  observation.  Had  there  been 
any  permanently  inhabited  spot  upon  the  Sierra  at  a  higher  elevation  than 
Summit,  and  one  whose  absolute  altitude  could  have  been  ascertained 
without  too  great  expense,  steps  would  have  been  taken  to  collect  obser- 
vations there,  with  the  view  of  preparing  special  tables  of  corrections  for 
the  highest  points ;  but  the  establishment  of  an  independent  station  upon 
the  mountains  for  meteorological  purposes  alone,  would  have  been  attended 
with  an  expenditure  far  exceeding  the  amount  of  money  available  for  such 
purposes.  It  is  only  upon  extensive  national  surveys,  liberally  equipped 
in  all  respects,  that  the  difficulties  can  be  overcome,  and  an  inquiry  of 
this  nature  successfully  prosecuted.  In  Colorado,  where  the  Eocky  Moun- 
tains attain  their  greatest  altitude,  it  has  been  possible  to  run  a  line  of 
levels  to  a  point  over  fourteen  thousand  feet  above  the  level  of  the  sea, 
and  to  maintain  at  this  great  elevation  a  permanent  station  for  regular 
observations,  with  corresponding  ones  at  lower  altitudes,  all  under  the 
management  and  control  of  Professor  Hayden  and  Mr.  Gardner,  of  the 
Geological  Survey  of  the  Territories. 

When  the  mass  of  material  collected  at  these  high  stations  has  been 
reduced  to  order,  and  the  necessary  computations  have  been  made,  it  is 
clear  that  practical  tables  of  corrections  will  result,  which  will  be  of  im- 
mediate use  in  all  barometrical  work  undertaken  in  the  interior  of  the 
continent.  There  will  still  be  a  question  how  far  they  are  applicable  to 
the  Sierra  Nevada  and  the  mountains  of  the  Pacific  coast ;  but  they  will 
certainly  indicate  whether  a  greater  or  less  deviation  from  the  truth  is  to 


CORRECTIONS  FOR  CALIFORNIA.  43 

be  expected  in  the  higher  mountain  regions,  and  what  ground  there  is 
for  the  belief  that  the  error  of  barometric  measurements  for  each  thou- 
sand feet  is  less  when  both  barometers  are  at  high  altitudes  than  when 
the  lower  one  is  considerably  nearer  the  level  of  the  sea.  That  the  com- 
puted difference  of  altitude  between  two  high  points  will  vary  with  the 
hour  of  the  day  at  which  the  observations  are  taken  there  can  be  no 
doubt;  but  it  seems  probable  that  the  daily  range  of  error  will  be  com- 
paratively small,  and  that  a  trained  observer  can  so  estimate  the  effects 
of  disturbances  in  the  atmosphere  as  to  select  the  most  favorable  point 
of  time  for  his  measurements  of  the  higher  peaks.  It  must  also  be  un- 
derstood that  in  California  by  far  the  greater  number  of  points,  the  accu- 
rate determination  of  whose  altitude  would  aid  materially  in  the  solution 
of  geological  problems,  lie  at  a  lower  altitude  than  eight  thousand  feet; 
and  thus  the  necessity  of  extending  the  investigation  to  the  higher  points 
was  less  pressing.  The  exact  altitude  of  the  highest  peaks,  though  very 
desirable  to  know,  cannot  be  definitely  ascertained  except  with  aid  of 
more  extended  series  of  observations. 

For  altitudes  between  three  thousand  and  five  thousand  feet,  the  station 
of  reference  being  still  supposed  to  be  in  the  valley,  there  is  room  for 
doubt  whether  Table  XXIII.  or  XXIV.  should  be  recommended.  Prob- 
ably, in  the  majority  of  cases,  some  correction  between  those  given  in  the 
two  tables  would  be  most  near  the  truth;  and  the  computer  should  be 
guided  by  the  general  character  of  the  climate  of  the  special  district  in 
which  the  observations  are  made.  If  this  resembles  that  of  the  moun- 
tains more  than  that  of  the  foot-hills  a  greater  weight  should  be  allowed 
to  Table  XXIV. ;  in  the  opposite  case  to  Table  XXIII.  Additional  ob- 
servations are  needed  before  this  point  can  be  treated  more  positively. 

If  the  lower  station  be  established  at  some  point  between  two  and 
three  thousand  feet  high,  Table  XXV.  can  be  used  in  the  same  way  as 
the  two  preceding;  and  probably  no  important  error  would  be  introduced 
by  extending  its  application  to  altitudes  of  eight  thousand  feet  or  a  little 
more. 

Illustrations  of  the  practical  use  which  can  be  made  of  the  tables  are 
shown  in  the  examples  below.  They  are  not  selected  for  any  striking 
peculiarity  or  for  their  proving  in  any  extraordinary  degree  the  value  of 
the  tables.  It  happens  only  that  they  are  the  first  computations  which 


44 


BAROMETRIC   HYPSOMETRY. 


have  been  made  since  the  tables  were  finished,  and  almost  the  only 
cases  in  which  the  tabular  correction  has  been  applied  to  any  published 
altitude.  The  issuing  of  a  new  edition  of  the  Yosemite  Guide-Book  was 
the  occasion  of  a  revision  of  (he  principal  statements  concerning  the  alti- 
tude of  important  places  mentioned,  and  the  opportunity  was  taken  to 
make  an  application  of  the  results  derived  from  the  labors  of  the  three 
years.  It  is  not  to  be  expected  that  the  corrections  will  remedy  all 
the  deficiencies  of  barometric  measurements,  for  it  would  be  seldom  the 
case  that  the  error  of  any  single  observation  would  be  just  balanced  by 
a  correction  based  upon  the  mean  of  a  long  series.  The  most  that  can 
be  looked  for  is  a  better  agreement  among  themselves  of  the  altitudes 
computed  from  observations  taken  in  different  conditions  of  the  atmos- 
phere, and  a  closer  approximation  to  the  truth  than  would  be  attained 
if  the  corrections  were  neglected.  That  these  ends  are  gained  is  quite 
evident  from  the  examples  cited.  The  first  example  is  that  of  the 
Yosemite  Valley. 

COMPUTED  ALTITUDE  OF  THE  BOTTOM  OF  YOSEMITE  VALLEY. 


Date. 

Corresponding 
Station. 

A 

B 

c 

D 

E 

F 

G 

1867  May  30  7  A.M. 

Summit 

3042.2 

3974.8 

+  18.4 

+     9.C 

3051.2 

3965.8 

+  18.3 

"    May  30  2  P.M. 

Summit 

3081.4 

3935.6 

-  20.8 

-  75.4 

3006.0 

4011.0 

+  63.5 

"    June  

Sacramento 

4046.0 

+  89.6 

-112.0 

3934.0 

13.5 

"    Oct  

Sacramento 

3935.0 

-  21.4 

+  34.0 

3969.0 

+  21.5 

1873  July  20   3  P.M. 

Sacramento 

4002.5 

4030.5 

f  74.1 

-111.2 

3891.3 

3919.3 

-  28.2 

"    July  20   3  P.M. 

Colfax 

1634.0 

4061.0 

+104.6 

-  42.7 

1591.3 

4018.3 

+  70.8 

"    July  20  3  P.M. 

Summit 

3170.4 

3846.6 

-109.8 

-  83.0 

3087.4 

3929.6 

-  17.9 

"    July  21   7A.M. 

Sacramento 

3845.3 

3873.3 

-  83.1 

0 

3845.3 

3873.3 

-  74.1 

"    July   21   7A.M. 

Colfax 

1465.7 

3892.7 

-  63.7 

+     7.2 

1472.9 

3899.9 

-  47.6 

"    July  21   7A.M. 

Summit 

3048.2 

3968.8 

+  12.4 

+  14.4 

3062.6 

3954.4 

+     6.9 

The  first  column  gives  the  date  of  the  observations  in  the  valley, 
and  the  second  the  station  at  which  corresponding  observations  were 
taken.  The  exact  position  of  the  barometer  at  Summit  in  1867  can  no 
longer  be  determined,  but  it  will  be  near  enough  for  the  present  pur- 
pose to  adopt  7,017  feet  as  its  approximate  altitude,  though  probably 
that  number  is  a  little  too  small. 

Column   A   contains   the   computed   difference   of  altitude,   uncorrected 


CORRECTIONS  FOR  CALIFORNIA.  45 

for  the  season  of  the  year,  between  the  valley  and  the  respective 
stations. 

Column  B  contains  the  different  values  for  the  altitude  of  the  valley 
above  the  sea,  obtained  from  the  results  in  column  A.  The  mean  of 
column  B  is  3956.4  feet. 

Column  C  shows  the  wanderings  from  the  mean  of  the  numbers  in  B. 
These  cannot  be  looked  upon  as  representing  exactly  the  errors  of  the 
respective  measurements,  for  the  absolute  altitude  of  the  valley  is  not 
known  from  other  than  barometrical  data.  The  extreme  difference 
amounts  to  214.4  feet. 

In  column  D  are  given  the  corrections  taken  from  the  new  tables, 
which  are  to  be  applied  to  the  numbers  in  column  A.  The  correction 
for  June,  1867,  is  based  upon  the  general  information  that  the  observa- 
tions were  taken  in  the  middle  of  the  day,  and  that  for  October  upon 
the  probability  that  the  mean  of  the  day  was  used  by  Colonel  William- 
son, who  made  the  computations. 

Columns  E  and  F  contain  the  corrected  values  of  the  numbers  in  A 
and  B.  According  to  these  values  the  altitude  of  the  valley  is  3947.5 
feet,  only  8.9  feet  less  than  the  altitude  obtained  without  the  use  of  the 
corrections.  This  approach  to  coincidence  is  accidental,  and  speaks  nei- 
ther for  nor  against  the  justness  of  the  corrections. 

Column  G  shows  the  wanderings  from  the  mean  of  the  values  in  F. 
These  wanderings  are  still  considerable,  but  the  maximum  difference  has 
been  reduced  to  144.9  feet. 

On  the  whole,  this  example  is  one  of  the  most  unfavorable  that  could 
be  cited.  The  Yosemite  Valley  lies  at  an  altitude  of  about  3,950  feet 
above  the  sea,  and  thus  falls  into  the  doubtful  region  for  which  the 
tables  of  corrections  are  not  perfectly  adapted;  and,  besides,  it  must  be 
allowed  that  observations  taken  upon  the  narrow  strip  of  comparatively 
level  land  which  lies  between  the  nearly  vertical  bounding  walls  of  the 
valley  would  naturally  be  more  or  less  affected  by  the  physical  pecu- 
liarities of  the  place. 

The  two  following  cases  will  be  seen  to  show  the  worth  of  the  new 
tables  in  a  more  favorable  light.  The  different  columns  are  designated 
in  the  same  way  as  the  corresponding  columns  in  the  example  just 
given. 


46 


BAROMETRIC   HYPSOMETRY. 


For  the  Tuolumne  Canon  the  use  of  the  corrections  has  reduced  the 
computed  altitude  from  7809.6,  the  mean  of  column  B,  to  7770.2  feet, 
the  mean  of  column  F ;  and  the  maximum  difference  between  any  two 
results  has  fallen  from  323.3  to  167.5  feet;  that  is  to  say,  by  not  quite 
fifty  per  cent,  though  more  than  in  the  case  of  the  Yosemite  Valley. 

COMPUTED  ALTITUDE   OF   CAMP   IN   TUOLUMNE   CANON,   NEAR  VIRGINIA   PASS 

TRAIL. 


Date. 

Corresponding 
Station. 

A 

B 

c 

D 

E 

F 

G 

1873  July  28  7  A.M. 

Sacramento 

7603.3 

7631.3 

-178.3 

+  87.4 

7690.7 

7718.7 

-51.5 

"    July  28  TA.M. 

Colfax 

5281.2 

7708.2 

-101.4 

+  29.5 

5310.7 

7737.7 

-32.5 

"    July  28  1  P.M. 

Sacramento 

7907.1 

7935.1 

+125.5 

-130.6 

7776.5 

7804.5 

+34.3 

"    July  28  1  P.M. 

Colfax 

5527.6 

7954.6 

+145.0 

-145.3 

5382.3 

7809.3 

+39.1 

"    July  29  7A.M. 

Sacramento 

7735.9 

7763.9 

-  45.7 

+  88.6 

7824.5 

7852.5 

+82.3 

"    July  29  7  A.M. 

Colfax 

5228.5 

7655.5 

-154.1 

+  29.5 

5258.0 

7685.0 

-85.2 

«    July  29  IP.M. 

Sacramento 

7902.6 

7930.6 

+121.0 

-130.6 

7772.0 

7800.0 

+29.8 

"    July  29   1  P.M. 

Colfax 

5471.0 

7898.0 

+  88.4 

-144.0 

5327.0 

7754.0 

-16.2 

The  effect  of  the  corrections  for  Peregoy's  is  to  reduce  the  extreme  dif- 
ference from  96.1  to  13.1  feet,  a  larger  reduction  than  could  be  hoped 
for  in  the  great  majority  of  cases.  The  computed  altitude,  6978.0  feet, 
has  been  in  this  case  increased  to  7000.4  feet. 


COMPUTED   ALTITUDE   OF  PEREGOY  S. 


Date. 

Corresponding 
Station. 

A 

B 

c 

D 

£ 

F 

G 

1873  July  197  P.M. 

Sacramento 

6959.7 

6987.7 

+     9.7 

+  12.6 

6972.3 

7000.3 

-     0.1 

"    July  19    7  P.M. 

Colfax 

4594.7 

7021.7 

+  43.7 

-  14.0 

4580.7 

7007.7 

+     7.3 

"    July  20  7  A.M. 

Sacramento 

6897.6 

6925.6 

-  52.4 

+  69.0 

6966.6 

6994.6 

-     5.8 

"    July  20  7  A.M. 

Colfax 

4550.2 

6977.2 

-     0.8 

+  21.6 

4571.8 

6998.8 

-     1.6 

In  these  examples  the  exhibit  is  made  the  more  unfavorable,  because, 
in  nearly  every  instance,  single  observations  have  been  computed  inde- 
pendently, and  the  wandering  of  each  one  from  the  mean  shown.  If  a 
different  course  had  been  followed,  and  the  mean  of  the  two  successive 
mornings,  for  instance,  in  the  Tuolumne  Canon,  been  taken  as  the  prob- 
able morning  average,  the  result  would  have  given  stronger  evidence  of 


CORRECTIONS  FOR  CALIFORNIA. 


47 


the  usefulness  and  necessity  of  applying  the  corrections  from  the  new 
tables.  To  show  this  more  clearly  the  following  table  is  added,  in  which 
the  mean  of  the  results  for  two  successive  days  is  given  for  each  of 
the  hours. 

COMPUTED  ALTITUDE   OF   CAMP   IN   TUOLUMNE   CANON. 
Mean  of  two  days. 


Date. 

Corresponding 
Station. 

Uncorrected. 

Corrected. 

1873  July,  7  A.M. 

Sacramento 

7697.6 

-112.0 

7785.6 

+  15.4 

July,   7  A.M. 

Colfax 

7681.8 

-127.8 

7711.3 

-  58.9 

July,   1  P.M. 

Sacramento 

7932.9 

+123.3 

7802.3 

+  32.1 

July,   1  P.M. 

Colfax 

7926.3 

+116.7 

7781.6 

+  11.4 

The  reduction  of  the  maximum  variation  is  consequently  from  251.1 
to  91.0  feet,  or  nearly  64  per  cent. 

Any  higher  degree  of  accuracy  in  the  determination  of  altitudes  than 
that  illustrated  by  the  examples  now  given  seems  scarcely  attainable  by 
the  use  of  the  barometer,  unless  the  observations  can  be  continued  for  a 
considerable  time  at  the  two  points  whose  difference  of  altitude  is  wished ; 
and  not  even  then,  unless  attention  be  paid  to  the  season  of  the  year 
and  the  hours  of  the  day  at  which  the  observations  are  taken.  But 
when  these  precautions  are  observed  and  the  proper  allowance  is  made 
for  the  special  circumstances  attending  each  case,  there  is  no  doubt  that 
the  barometer  furnishes  the  readiest  means  of  ascertaining  the  altitudes 
of  elevated  points,  with  little  labor  and  only  moderate  expense,  to  with- 
in very  narrow  limits  of  error. 

It  is,  in  fact,  indispensable  upon  surveys  in  wild  and  mountainous  re- 
gions, if  the  estimates  of  heights  are  to  be  anything  better  than  guess- 
work. The  use  of  the  spirit-level,  or  similar  instrument  of  precision, 
would  be  entirely  out  of  the  question,  not  merely  from  the  attendant 
expenses  and  the  amount  of  time  required  to  run  the  lines,  but  also 
from  the  difficulty  of  carrying  the  instrument  up  the  steepest  slopes, 
where  oftentimes  even  the  barometer  strapped  to  the  back  begins  to  be 
a  serious  hindrance  to  progress  in  the  ascent.  It  needs,  perhaps,  to  be 
dwelt  upon  with  more  than  usual  emphasis  in  this  place,  after  what  has 
been  written  of  the  imperfections  of  this  method  of  measurement,  that  the 
barometer,  for  purposes  of  hypsometry,  holds  a  position  peculiarly  its  own. 


48 


BAROMETRIC  HYPSOMETRY. 


It  can  make  no  claim  to  unfailing  accuracy,  but,  when  used  with  judg- 
ment and  with  proper  attention  to  details  of  time  and  place,  it  gives 
results  which  are  very  near  the  truth,  and  which  cannot  be  reached  by 
any  other  means  at  the  command  of  the  surveyor  or  explorer.  The 
object  of  the  present  discussion  is  not  to  weaken  confidence  in  baro- 
metric work,  but  to  show  in  what  way  it  may  be  carried  on  so  as  to 
yield  the  best  results  and  contribute  the  most  trustworthy  information 
about  some  of  the  most  prominent  features  in  the  physical  geography  of 
the  elevated  regions  of  the  globe. 

For  points  whose  difference  of  altitude  is  not  great,  however,  no  very 
close  approximation  to  the  truth  ought  to  be  expected,  particularly  if  the 
stations  lie  on  opposite  sides  of  mountain  ranges  and  show  any  marked 
dissimilarity  of  climate.  This  will  appear  very  strikingly  from  an  ex- 
amination of  the  following  table,  which  shows  the  computed  difference 
of  altitude  between  the  barometer  at  Mr.  Freeman's  house  on  L  Street, 
Sacramento,  and  the  station  barometer  at  No.  91  Montgomery  Block, 
San  Francisco,  for  the  first  seven  months  of  the  year  1871,  the  only 
period,  during  the  three  years  covered  by  the  investigation,  at  which 
observations  could  be  kept  up  with  regularity  at  the  San  Francisco  office 
of  the  Survey.  The  observer  for  these  seven  months  was  Mr.  Charles 
Eabe.  The  barometer  at  San  Francisco  was  known  to  be  twenty-eight 
feet  above  that  at  Sacramento.  The  table  also  shows  the  deviation  of  the 
computed  results  from  the  truth. 

COMPUTED  ALTITUDE   OF  NO.  91   MONTGOMERY   BLOCK,   SAN   FRANCISCO, 
ABOVE   L   STREET,   SACRAMENTO. 


Date. 

7  A.  M. 

2  P.M. 

9  P.M. 

Mean. 

1871  January 

57.3 

+29.3 

47.7 

+19.7 

35.3 

+  7.3 

4G.9 

+18.9 

February 

44.8 

+16.8 

49.7 

+21.7 

38.1 

+10.1 

43.G 

+15.6 

March 

29.0 

+  1.0 

38.2 

+10.2 

13.8 

-14.2 

26.7 

-  1.3 

April 

19.1 

-  8.9 

18.7 

-  9.3 

3.7 

-24.3 

13.9 

-14.1 

May 

19.3 

-  8.7 

7.4 

-20.6 

9.2 

-18.8 

12.2 

-15.8 

June 

2.9 

-25.1 

-  5.7 

-33.7 

-20.6 

-48.6 

-  8.5 

-36.5 

July 

-  4.7 

-32.7 

-20.2 

-48.2 

-25.3 

-53.3 

-16.0 

-44.0 

The  effect  of  the  heat  in  the  Sacramento  Valley  in  expanding  the  air 
and   diminishing   the   pressure,   so   that  the   barometer   stands   uniformly 


CORRECTIONS   FOR   CALIFORNIA. 


49 


lower,  though  actually  nearer  the  sea-level,  at  Sacramento  than  at  San 
Francisco  during  midsummer,  is  made  very  manifest  by  the  minus  signs 
in  the  results  for-  June  and  July.  Were  there  no  other  sources  of  in- 
formation than  barometric  observations  in  these  months,  it  would  be 
admitted  by  every  one  that  the  streets  of  Sacramento  must  stand  at  a 
higher  level  than  the  upper  stories  of  high  buildings  on  Montgomery 
Street,  San  Francisco.  The  cause  of  this  is  to  be  looked  for  chiefly  in 
the  extraordinary  differences  in  the  range  of  temperature  at  the  two  places. 
For  the  seven  months  in  question  the  lowest  recorded  temperature  at 
San  Francisco  was  42°.3,  January  12,  7  A.  M. ;  and  the  highest,  75°,  June 
6,  2  P.  M.  At  Sacramento  the  range  was  from  31°,  January  11,  7  A.  M., 
to  101°.5,  June  29,  2  p.  M.,  —  more  than  double  the  extreme  variation  at 
San  Francisco. 

The  tables  of  corrections  whose  construction  and  use  have  now  been 
described  will  not,  of  course,  be  strictly  applicable  for  cases  which  fall 
entirely  outside  the  limits  for  which  they  were  calculated.  Could  simi- 
lar tables,  based  upon  observations  in  other  countries  or  other  parts  of 
this  country,  be  brought  side  by  side  with  these  for  comparison,  there 
would  doubtless  be  in  all  instances  a  general  similarity  in  the  main 
features,  accompanied  by  such  decided  differences  in  the  numerical  values 
of  the  corrections,  that  no  single  table  could  be  adopted  for  universal 
use.  *  For  the  sake  of  illustrating  these  differences  the  two  following 
tables  are  added  to  give  an  idea  of  what  might  have  been  expected  if 
San  Francisco  instead  of  Sacramento  had  been  chosen  for  the  lower 
station  of  reference. 

SAN   FRANCISCO   AND   COLFAX. 
True  difference  of  altitude  2371  feet. 


Date. 

7A.M. 

2  P.M. 

9  P.M. 

Mean. 

1871  January 

2322.3 

-48.7 

2382.6 

+11.6 

2343.9 

-27.1 

2349.4 

-21.6 

February 

2349.0 

-22.0 

2385.4 

+14.4 

2376.5 

+  5.5 

2370.5 

-  9.5 

March 

2375.5 

+  4.5 

2408.9 

+37.9 

2382.5 

+11.5 

2389.0 

+18.0 

April 

2375.2 

+  4.2 

2422.1 

+51.1 

2376.5 

+  5.5 

2391.1 

+20.1 

May 

2399.7 

+28.7 

2443.3 

+72.3 

2391.2 

+20.2 

2411.3 

+40.3 

June 

2393.4 

+22.4 

2448.2 

+77.2 

2378.9 

+  7.9 

2407.4 

+36.4 

July 

2410.9 

+39.9 

2455.2 

+84.2 

2396.1 

+25.1 

2420.0 

+49.0 

*  Compare  Chapter  III.,  page  63. 


50 


BAROMETRIC  HYPSOMETRY. 


SAN   FRANCISCO  AND   SUMMIT. 
True  difference  of  altitude  6961  feet. 


Date. 

7  A.  M. 

2  P.M. 

9  P.M. 

Mean. 

1871  January 

6799.0 

-162.0 

6930.2 

-30.8 

6837.1 

-123.9 

6855.5 

-105.5 

February 

6871.4 

-  89.6 

6999.4 

+38.4 

6909.6 

-  51.4 

6927.0 

-  34.0 

March 

6906.2 

-  54.8 

7018.7 

+57.7 

6902.8 

-  58.2 

6942.9 

-  18.1 

April 

6930.8 

-  30.2 

7038.0 

+77.0 

6872.2 

-  88.8 

6946.6 

-  14.4 

May 

6956.7 

-    4.3 

7047.5 

+86.5 

6878.7 

-  82.3 

6961.2 

+    0.2 

June 

6901.1 

-  59.9 

7016.2 

+55.2 

6827.4 

-133.6 

6915.9 

-  45.1 

July 

6855.2 

-105.8 

6993.5 

+32.5 

6817.7 

-143.3 

6888.8   -  72.2 

The  series  is  so  short  that  a  detailed  discussion  of  its  peculiar  features 
is  unnecessary  and  would  lead  to  no  practical  results,  and  it  is  to  be  re- 
gretted that  the  material  is  not  at  hand  for  comparing  the  results  of  an 
entire  year.  The  chief  points  of  interest  will  be  detected  at  once  by  a 
comparison  with  Tables  I.  and  IV.,  portions  of  which  relate  to  the  same 
period  of  time. 


CHAPTER    III. 

RESUME  OF  SIMILAR  INVESTIGATIONS  OUTSIDE  OF  CALIFORNIA. 

IN"  the  introductory  chapter  a  condensed  account  has  been  given  of  the 
principal  modifications  which  have  been  made,  or  proposed,  in  the  baro- 
metric formula,  for  the  sake  of  bringing  the  results  obtained  by  its  use 
into  a  closer  agreement  with  the  truth.  It  is  there  mentioned  that  the 
occurrence  of  unexpectedly  large  discrepancies  in  the  heights  of  impor- 
tant points,  when  the  measurements  are  made  in  different  seasons  of  the 
year,  or  in  different  conditions  of  the  atmosphere  of  whatever  nature, 
has  attracted  the  attention  of  observers  from  time  to  time;  and  it  is 
further  shown  that  no  change  in  the  formula  has  been  able  to  remedy 
the  difficulty  entirely.  Improved  determinations  of  the  values  of  the  con- 
stant factors,  and,  for  computations  based  upon  extended  series  of  observa- 
tions, the  introduction  of  a  special  term  for  the  effect  of  the  aqueous 
vapor  in  the  atmosphere,  added,  it  is  true,  to  the  degree  of  accuracy 
attainable  and  reduced  the  discrepancies  in  part;  but  the  differences  in 
the  results  still  remained  too  great  to  be  explained  solely  as  errors  of 
observation,  and  were  of  such  a  nature  that  they  could  not  properly  be 
charged  to  deficiencies  in  the  formula. 

It  is  the  object  of  the  present  chapter  to  give  in  a  concise  form  a  com- 
parative view  of  the  principal  suggestions  which  have  been  made  for 
eliminating  or  avoiding  these  residual  errors,  and  to  show  that  the  method 
followed  in  the  California  investigation  is  the  one  which  leads  most  di- 
rectly to  practical  results,  and  upon  which  the  chief  dependence  is  to  be 
placed. 

As  early  as  1806,  Ramond*  published  a  memoir  in  which  he  attributed 

*  Memoires,  etc. ,  pp.  39  -  59. 


52  BAROMETRIC   HYPSOMETRY. 

the  discordance  of  results  obtained  by  different  observers  to  the  influence 
of  the  hour  of  the  day,  the  influence  of  locality,  and  the  influence  of  the 
winds  and  air-currents.  The  change  from  hour  to  hour,  or  the  daily  vari- 
ation, he  considered  the  most  important,  and  proved  its  existence  by  citing 
the  means  of  altitudes  computed  from  observations  taken  at  different  hours 
from  six  in  the  morning  to  ten  at  night  at  Bagneres  and  at  Bareges,  when 
compared  with  synchronous  observations  taken  by  Dangos  at  Tarbes.  His 
comments  upon  the  observed  facts,  almost  literally  translated,  are  as  fol- 
lows :  — 

"Seven  or  eight  hundred  observations  of  this  kind,  each  calculated 
separately,  have  shown  constantly  the  same  sort  of  variation.  The  seasons 
of  the  year  and  the  differences  of  locality  have  introduced  no  changes 
except  in  the  range  of  the  variation.  At  the  tops  of  mountains,  on  plains, 
or  in  the  depths  of  valleys,  observations  in  the  forenoon  and  the  afternoon 
have  led  to  results  which  are  smaller  just  in  proportion  to  the  length  of 
time  between  midday  and  the  actual  moment  of  observation;  although 
it  is  not  precisely  at  the  hour  of  noon  that  the  maximum  results  are 
found.  The  computed  altitudes  continue  increasing  until  towards  one  or 
two  o'clock,  a  little  earlier  or  a  little  later;  but  both  the  amount  of  the 
increase  and  the  time  of  reaching  the  maximum  depend  largely  upon  the 
season  of  the  year,  the  clearness  of  the  day,  and  perhaps  the  direction 
of  the  wind.  A  small  part  of  this  daily  variation  can  be  attributed  to  the 
hygrometric  state  of  the  atmosphere,  and  it  would  not  be  difficult  to  in- 
troduce into  the  calculation  a  correction  for  the  humidity  of  the  air;  but 
the  largest  part  of  the  error  results,  without  doubt,  from  a  cause  much 
more  powerful  and  much  more  difficult  to  estimate;  to  wit,  the  influence 
of  ascending  and  descending  currents  of  air  which  act  both  upon  the 
barometer  and  thermometer,  either  in  diminishing  or  increasing  the  weight 
of  the  air-column,  according  to  their  velocity  and  direction,  or  in  bringing 
from  an  upper  or  lower  region  a  temperature  which  does  not  belong  by 
right  to  the  place  where  the  observation  is  made.  Such  disturbances  are 
essentially  anomalous,  ....  and  there  is  no  other  resource  than  to  avoid 
tb.3  hours  where  their  interference  is  most  common.  The  hours  of  the 
middle  of  the  day  are  the  least  affected,  and  among  these  the  hour  of 
noon  has  this  particular  advantage,  that  the  heights  which  it  gives  are 
sufficiently  near  the  mean  of  those  which  are  obtained  from  observations 


WORK  OUTSIDE  OF  CALIFORNIA. 


53 


made  within  the  limits  of  three  or  four  hours  which  are  included  in 
the  short  period  of  equilibrium." 

As  to  the  influence  of  locality,  Eamond  advises  that  the  barometer 
should  be  observed,  when  possible,  upon  the  summit  of  isolated  peaks; 
for  the  more  complete  the  isolation  the  less  will  the  observations  be 
affected  by  local  causes  of  disturbance.  In  particular,  he  shows  the  com- 
parative untrustworthiness  of  the  barometer  as  an  instrument  for  determin- 
ing small  differences  of  altitude  in  level  countries. 

The  discussion  of  the  influence  of  the  winds  was  taken  up  by  Eamond 
at  considerable  length,  and  the  conclusion  reached  that  the  computed 
heights  would  be  too  high  when  the  wind  blew  strongly  from  the  north, 
and  too  low  when  strong  southerly  winds  prevailed. 

In  a  subsequent  memoir,  published  in  1808,  Eamond  appears  to  have 
made  a  partial  study  of  the  annual  variation  in  barometric  measurements, 
without  dwelling  upon  it  in  much  detail.  He  says :  *  "  Experience  has 
taught  me  that  each  month  and  each  season  exercises  its  influence  upon 
the  instruments.  It  was  natural  to  look  upon  the  revolution  of  the  four 
seasons  as  a  cycle,  in  which  the  greater  part  of  the  compensations  would 
manifest  themselves,  and  I  have  become  convinced  that  the  space  of  a 
year  cannot  be  arbitrarily  lengthened  or  shortened,  without  making  the 
distinctive  character  of  the  particular  season  predominate  in  the  result." 
Under  Eamond's  direction  observations  were  taken  at  noon  of  each  day, 
with  only  occasional  omissions,  for  two  years  at  Clermont,  in  Central 
France,  and  at  Paris.  The  observations  began  in  1806,  and  closed  in 
1808.  The  observations  were  computed  separately,  and  the  means  for 
each  month,  translated  into  English  measure,  are  given  in  the  table 
below. 

COMPUTED   DIFFERENCE   OF  ALTITUDE   BETWEEN   PARIS  AND   CLERMONT. 


January  

1110.3 
1031.5 
1157.2 
1127.6 
1107.0 
1145.4 

+  13.9 

64  9 

Jill  V 

1112.9 

1128.3 
1103.4 
1106.3 
1046.9 
980.3 

+  16.5 
+  31.9 
+     7.0 
+     9.9 
-   49.5 
-116.1 

February  
March  

Auorist  

+  60.8 
+  31.2 
+  10.6 
+  49.0 

September  
October 

April  

Mav  .. 

November  
December  

June  

*  Memoires,  etc.,  p.  71. 


54  BAROMETRIC   HYPSOMETRY. 

The  mean  value  for  the  year,  1096.4  feet,  was  adopted  as  the  true 
difference  of  altitude  between  the  two  stations.  The  table  shows  decided 
differences  in  the  different  months,  and  the  average  for  the  six  months 
of  spring  and  summer  is  ove*r  sixty-five  feet  more  than  the  average  for 
the  six  months  of  autumn  and  winter,  but  the  change  from  month  to 
month  is  not  so  regular  as  might  have  been  expected;  and  Eamond, 
probably  on  account  of  this  irregularity,  did  not  publish  any  directions 
which  relate  to  the  best  season  of  the  year  in  which  to  make  measure- 
ments. 

In  the  concluding  remarks  to  his  third  memoir  he  says:*  "Eesults  as 
satisfactory  as  they  have  been  unexpected  have  been  the  reward  of  my 
labor.  I  have  seen  a  wonderful  agreement  established  between  the 
changes  of  the  atmosphere  and  the  errors  which  appeared  at  first  anom- 
alous ;  I  have  seen  the  one  serve  as  an  index  and  sometimes  as  a  measure 
of  the  other,  and  all  reduced  to  a  small  number  of  general  effects,  which 
themselves  spring  from  a  common  cause;  and  now  a  very  simple  and 
homogeneous  theory  binds,  in  my  mind,  all  the  phenomena  together. 
The  surface  of  the  atmosphere  tends  constantly  to  a  level  form,  and  the 
weight  of  the  air-columns  varies  with  the  changes  which  take  place  in 
the  density  of  their  strata.  Variations  in  temperature  are  the  principal 
cause  of  these  changes  of  density.  Every  change  of  temperature  causes 
a  wind  or  springs  from  a  wind,  which  conveys  from  one  place  to  another 
the  temperature  and  density  which  it  received  at  its  origin.  These  cur- 
rents of  air  can  have  only  three  directions  with  respect  to  the  surface  of 
the  earth :  they  are  vertical,  inclined,  or  horizontal.  When  they  assume 
the  latter  direction,  they  act  by  the  difference  which  exists  between  their 
density  and  that  of  the  layers  they  replace.  When  they  follow  one  of 
the  first  two  directions,  the  effect  of  the  velocity  of  ascent  or  descent  is 
combined  with  that  of  the  density." 

The  words  of  Eamond  have  been  thus  freely  quoted  because  they  con- 
tain the  first  clear  statement  of  the  existence  of  a  diurnal  period  in  baro- 
metric measurements.  The  similar  observations  made  by  Deluc  in  the 
previous  century  had  rested  upon  a  poorer  foundation,  and  the  low  results 
obtained  at  sunrise  were  thought  by  him  to  be  caused  by  the  easterly 

*  Memoires,  etc.,  pp.  116-119. 


WORK   OUTSIDE   OF   CALIFORNIA.  55 

winds  prevailing  at  that  hour;  for,  when  the  wind  blew  from  any  other 
direction,  the  discrepancy  was  less.*  Eamond's  belief  that  observations  at 
noon  were  in  all  cases  the  most  to  be  relied  upon,  and  his  advice  to  con- 
fine them  entirely  to  that  hour,  would,  if  adopted,  materially  abridge  the 
usefulness  of  the  barometer  upon  geological  and  topographical  surveys; 
for  it  is  not  generally  in  the  power  of  the  explorer  to  be  upon  the  spot 
whose  altitude  is  wished  at  just  the  hour  of  noon,  and,  besides,  it  is  now 
well  understood  that  neither  that  hour  nor  any  other  will  give  the  best 
approximation  in  all  the  months. 

That  there  is  an  annual  as  well  as  a  diurnal  variation  was  pointed  out 
by  D'Aubuissonf  much  more  satisfactorily  than  by  Eamond.  The  dif- 
ference of  altitude  between  Geneva  and  St.  Bernard,  computed  from  the 
mean  of  the  two-o'clock  observations  for  the  four  years  from  1818  to 
1821,  was  least  in  the  month  of  December,  and  increased  without  inter- 
ruption until  June,  in  which  month  it  was  at  its  maximum ;  it  then 
decreased  with  equal  regularity  until  December.  The  wandering  from  the 
mean  value  amounted  in  December  to  79,  and  in  June  to  92  feet,  making 
the  extreme  discrepancy  171  feet.  These  numbers  are  very  much  greater 
than  those  in  the  table  given  in  the  introductory  chapter,  page  24;  but 
it  must  be  remembered  that  those  results  came  from  means  of  the  day 
and  not  from  the  means  of  midday  alone.  The  more  modern  formulae, 
also,  make  the  range  of  error  between  summer  and  winter  less  than  the 
older  ones;  so  that  the  difference  between  the  two  cases  is  really  less 
than  might  be  expected,  if  anything  is  to  be  allowed  for  the  improvements 
in  the  construction  of  instruments  in  the  thirty  or  forty  years  intervening. 
D'Aubuisson  explains  both  the  diurnal  and  the  annual  variation,  not  by 
ascending  and  descending  currents  of  air,  as  Ramond  did,  but  by  the 
error  in  the  estimation  of  the  actual  mean  temperature  of  the  air-column 
when  this  is  taken  to  be  the  half-sum  of  the  extreme  temperatures,  and 
adds :  "  From  what  has  just  been  said  it  follows  that  our  temperature 
term  will  err  in  excess :  firstly,  at  those  hours  or  moments  of  the  day 


*  See  Suckow's  Barometrische  Hypsometric.     Darmstadt,  1843.     p.  51. 

t  D'Aubuisson's  Traite  de  Geognosie,  Paris,  1828,  Tom.  I.  p.  495.  The  same  topic  was  dis- 
cussed by  him  more  briefly  at  earlier  dates  in  contributions  to  the  Bibliotheque  Universelle  and 
other  periodicals. 


56  BAROMETRIC   HYPSOMETRY. 

when  the  temperature  at  the  surface  of  the  earth  rises  above  the  meau 
value,  aud  so  much  the  more  in  amount  the  more  rapid  or  considerable 
the  rise  is;  secondly,  when,  from  one  day  to  another,  a  notable  elevation 
of  temperature  prevails ;  thirdly,  in  the  hottest  season  of  the  year."  But 
he  despaired  of  being  able  to  separate  from  other  errors  of  observation 
those  which  belonged  to  the  temperature  term  alone,  and  confined  himself 
to  certain  comments  "  which  should  give  an  idea  of  the  influence  of  these 
variations  of  temperature  from  hour  to  hour,  from  day  to  day,  and  from 
season  to  season."  This  was  valuable  as  far  as  it  went,  and  served  as  a 
tolerable  measure  of  the  degree  of  accuracy  attainable  in  the  use  of  the 
barometer,  but  was  not  expected  to  lead  to  any  systematic  application 
of  corrections. 

The  diurnal  variation  in  barometric  measurements  was  also  made  a 
subject  of  investigation  by  Homer,  of  Zurich,  one  of  the  companions  of 
Krusenstern  in  his  voyage  around  the  world,  and  to  whom  so  much  credit 
is  due  for  his  contributions  to  Swiss  geography.  As  early  as  1813,  his 
attention  had  been  called  to  the  subject,  but  it  was  not  until  fourteen 
years  later  that  he  was  able  to  make  the  necessary  observations  under 
favorable  conditions.  In  August,  1827,  he  published  a  paper*  in  which 
was  given  in  detail  an  account  of  the  determination  of  the  height  of  the 
Eighi  above  Zurich,  both  trigonometrically  and  barometrically.  Between 
the  22d  of  January  and  the  1st  of  February,  1827,  118  synchronous  ob- 
servations at  Zurich  and  upon  the  top  of  the  mountain  were  obtained, 
and  each  computed  by  itself.  The  difference  of  altitude  from  the  mean 
of  observations  at  7  A.  M.  was  4161.6  feet,  and  the  increase  was  regular 
and  unbroken  until  1  P.  M.,  for  which  hour  the  computed  difference  was 
4221.6  feet.  The  extreme  variation,  therefore,  between  early  morning  and 
midday  amounted  to  about  y1^  of  the  total  height,  hardly  more  than 
half  the  amount  of  variation  for  the  corresponding  month  and  hours  in 
California,  as  will  appear  from  a  glance  at  Tables  X. -XII. 

The  work  was  taken  up  again  in  June  of  the  same  year,  and  166  syn- 
chronous observations  made  between  the  2d  and  the  17th  of  the  month. 
The  rise  from  morning  to  midday  and  the  fall  from  midday  to  evening  were 

*  Denkschriften  der  allgemeinen  Schweizerischen  Gesellschaft  fur  Naturwissenschaften. 
Band  1,  Zurich,  1833,  Abtheilung  2,  pp.  137-174. 


WORK   OUTSIDE   OF  CALIFORNIA.  57 

even  more  regular  than  in  January,  but  the  amount  of  variation  was 
different,  being  only  -fa  instead  of  YV,  and  the  maximum  value  was  given 
as  early  as  11  A.  M.  The  amount  of  variation  between  morning  and  noon 
was  found  by  Eamond  in  the  Pyrenees  to  amount  to  as  much  as  ^  of  the 
total  difference  of  altitude.* 

A  comparison  of  these  two  sets  of  results  showed  that  in  summer  the 
mean  of  all  the  observations  gave  a  result  higher  by  45.6  feet  than  the 
mean  of  the  winter  observations.  For  this  difference  Homer  suggested 
several  possible  explanations,  prominent  among  which  was  an  erroneous 
estimate  of  the  effect  of  the  aqueous  vapor  in  the  atmosphere;  but  he 
reached  no  satisfactory  conclusion,  and  proposed  at  that  time  no  means 
of  overcoming  the  difficulty.  For  the  true  difference  of  altitude  between 
Zurich  and  the  Eighi  he  depended  upon  trigonometrical  measurements. 
With  these  the  barometric  results  for  the  winter  season  agreed  in  the 
middle  of  the  day;  but  in  summer  the  hours  just  after  sunrise  or  before 
sunset  gave  the  most  accurate  results.  In  view  of  these  inequalities, 
Horner  pointed  out  the  great  danger  of  error  in  making  barometric  meas- 
urements, or  in  attempting  to  improve  the  coefficients  of  the  formula,  if 
dependence  was  placed  upon  observations  taken  without  any  regard  to 
times  or  seasons.  The  best  course  to  be  followed  was  also  indicated  by 
him  in  nearly  the  following  words  :  "  From  these  series  of  observations 
there  seems  to  be  proved  the  necessity  of  a  horary  correction,  and  possibly 
of  one  other,  which  shall  depend  upon  the  deviations  of  the  observed 
temperatures  from  the  mean  temperature  of  the  place."  The  results  under 
discussion  not  furnishing  sufficient  data,  the  further  development  of  this 
idea  had  to  be  postponed.  That  it  was  not  abandoned  is  proved  by  his 
having  left  among  his  papers  a  table  of  corrections  for  different  hours  of 
the  day  to  be  applied  to  the  computed  differences  of  altitude.  The  obser- 
vations upon  which  these  corrections  were  based  are  not  known,  but  the 
table  is  printed  in  part  by  Bravais,f  by  whom  it  was  seen  at  Zurich  in 
1842.  The  original  table  was  too  long  to  be  quoted  entire,  but  the  por- 
tion available  and  given  on  the  next  page  is  enough  to  show  the  line  of 
thought  upon  which  Horner  was  engaged.  It  will  be  observed  that  no 


*  Suckow's  Barometrische  Hypsometric,  p.  56. 
t  Comptes  Kendus,  Tom.  XXXI.,  1850,  p.  176. 


58 


BAROMETRIC   HYPSOMETRY. 


reference  is  here  made  to  the  season  of  the  year,  and  that  the  correction 
for  the  hour  of  the  day,  whether  positive  or  negative,  increases  much  more 
rapidly  than  the  altitude,  —  a  point  which  does  not  seem  to  have  heen 
well  established  by  later  observations.  In  the  original  table  the  heights 
and  corrections  are  all  given  in  toises. 

CORKECTIONS   TO   BE   APPLIED   TO   THE    COMPUTED   HEIGHTS. 


Height. 

12  M. 

IP.  M. 

2P.M. 

3P.M. 

4P.M. 

5P.M. 

6P.M. 

200 

-0.6 

-0.4 

-0.3 

-0.1 

+  0.1 

+  0.3 

+  0.5 

400 

-1.4 

-1.1 

-0.7 

-0.2 

-0.1 

+  0.6 

+  1.1 

600 

-2.4 

-1.8 

-1.3 

-0.4 

+  0.2 

+  1.1 

+  2.0 

800 

-3.7 

-2.8 

-2.0 

-0.6 

+  0.3 

+  1.7 

+  3.1 

1000 

-5.2 

-4.0 

-2.8 

-0.8 

+  0.5 

+  2.3 

+  4.4 

1200 

-7.0 

-5.4 

-3.7 

-1.1 

+  0.7 

+  3.2 

+  5.8 

The  horary  correction  proposed  by  Bravais  himself,  from  an  examina- 
tion of  the  observations  of  De  Saussure  and  of  Kaemtz,  were  as  follows :  — 


At  noon  subtract  ^  of  the  height. 

«    IP.  M.      "  ^        " 

"     2        «  "  T*ir       "  " 

«   3     " 
u   4     « 


tb 

TH  " 


"   5 
"  6 


*r    rt 


The  absence  of  any  reference  to  the  season  of  the  year  makes  this  table 
valueless  for  general  use,  though  it  served  the  special  purpose  for  which 
it  was  made  by  Bravais. 

The  investigations  of  Kaemtz  in  the  Alps  during  his  journeyings  there 
in  1832  *  also  reached  no  further  than  the  diurnal  variation,  as  no  atten- 
tion could  be  paid  to  the  annual  variation  on  account  of  the  shortness  of 
the  time  given  up  to  taking  observations.  The  points  at  which  he  made 
the  most  complete  series  of  observations  were  the  Eighi  and  the  Faulhorn ; 
referring  in  one  case  to  both  Zurich  and  Geneva,  and  in  the  other  to 
Zurich  alone.  His  method  of  ascertaining  the  true  value  of  the  correction 


*  PoggendorfFs  Annulen  der  Physik  und  Chemie,  Band  27,  1833,  pp.  345-361. 


WORK  OUTSIDE  OF  CALIFORNIA.  59 

for  each  hour  of  the  day  and  night  was  more  general  than  the  others 
which  have  been  referred  to.  He  employed  an  interpolation  formula  of 
the  form  which  is  commonly  used  in  meteorological  investigations,  where 
the  effects  of  periodicity  in  any  disturbing  cause  are  to  be  estimated. 
Letting  x  denote  the  mean  value  of  the  separate  hourly  results,  or  the 
true  difference  of  altitude,  and  Xn  the  true  result  for  the  nth  hour  after 
noon,  the  formula  takes  the  form, 

Xn  =  x  -f  a  sin  (n  15°  +  a)  +  6  sin  (2  n  15°  +  /3)  -f  c  sin  (3  n  15°  -f-  y), 

where  a,  b,  c,  are  numerical  coefficients  and  a,  /3,  y,  auxiliary  angles,  whose 
values  are  to  be  determined  so  as  to  make  the  results  calculated  from  this 
formula  agree  with  the  observed  results  for  those  hours  at  which  obser- 
vations were  actually  taken.  The  formula  will  then  hold  for  all  values  of 
n  from  1  to  24,  that  is,  for  every  hour  of  day  and  night,  and  can  be  used 
for  purposes  of  interpolation  and  for  ascertaining  the  times  at  which  the 
computed  altitudes  are  at  their  maximum,  minimum,  or  mean  values. 
Between  Zurich  and  the  Eighi  the  maximum  was  found  to  fall  about  half 
past  eleven  in  the  forenoon,  thus  agreeing  quite  closely  with  Homer,  and 
the  minimum  at  three  o'clock  in  the  morning.  The  mean  or  true  value 
was  obtainable  at  quarter  past  seven  in  the  morning  or  at  seven  in  the 
evening.  The  difference  between  the  maximum  and  the  minimum  values 
amounted  to  about  -£=%  of  the  total  difference  of  altitude. 

Similar  calculations  for  Zurich  and  the  Faulhorn  led  to  slightly  dif- 
ferent results.  The  hour  of  the  maximum  altitude  was  ten  minutes  before 
one  in  the  afternoon,  and  of  the  minimum,  quarter  past  four  in  the  morn- 
ing. The  extreme  variation  amounted  to  -^  of  the  true  elevation  of  the 
mountain  above  Zurich. 

"With  the  assistance  of  a  formula  of  this  kind  it  would  be  possible  to 
prepare  quite  full  tables  of  corrections,  but  it  does  not  appear  that  that 
was  any  part  of  the  purpose  which  Kaemtz  had  in  view;  and  even  if 
such  a  table  had  been  made,  its  measure  of  trustworthiness  would  be  just 
equal  to  that  of  the  observations  on  which  it  was  based,  and  its  applica- 
tion be  restricted  to  the  mountains  of  Switzerland.  Without  going  further 
into  the  details  of  the  facts  upon  which  Kaemtz  founded  his  opinion,  it 
may  be  added  that  he  believed  the  source  of  the  errors  to  lie  in  the  incor- 
rect estimation  of  the  real  mean  temperature  of  the  air-column,  when 


60  BAROMETRIC   HYPSOMETRY. 

this  is  assumed  to  be  equal  to  the  half-sum  of  the  two  temperatures 
observed  at  the  extreme  stations. 

The  formula  proposed  by  General  Baeyer,  as  has  been  mentioned  on 
page  21,  gave  results  which  reduced  in  some  measure  the  extreme  varia- 
tion between  morning  and  midday,  but  not  entirely.  His  published  ob- 
servations cover  only  a  part  of  one  day,  September  1,  1849,  but  they  .were 
taken  hourly,  and  were  computed  by  Laplace's  formula  as  well  as  by  his 
own,  so  that  the  comparative  value  of  the  two  formulae  is  clearly  shown. 
Between  Kupferkuhle  and  the  Brocken,  in  the  Hartz  Mountains,  whose 
difference  of  altitude,  ascertained  trigonometrically,  was  2,989  feet,  the 
extreme  variation  arising  from  the  use  of  Laplace's  formula  was  66.7,  and 
from  Baeyer's,  58.4  feet;  a  gain  too  slight  to  inspire  much  confidence  in 
the  proposed  new  form  for  the  temperature  term.  Baeyer's  advice  to  ob- 
servers is  to  take  the  mean  of  observations  between  ten  in  the  morning 
and  half  past  five  in  the  afternoon  as  the  best  approximation  to  the  truth, 
because  the  results  obtained  before  ten  o'clock  or  later  than  half  past  five 
are  too  low.  One  of  the  most  interesting  parts  of  Baeyer's  paper  shows 
that  the  same  causes  which  produce  the  diurnal  variation  in  the  barometer 
exert  a  like  influence,  though  in  the  opposite  direction,  upon  altitudes 
determined  trigonometrically,  the  morning  results  being  too  high  and 
those  of  midday  being  too  low. 

The  meteorological  observations  which  have  been  taken  at  Geneva  and 
St.  Bernard  have  furnished  abundant  material  for  a  much  more  thorough 
study  of  the  general  subject  of  barometric  measurements  than  has  been 
possible  in  any  of  the  cases  previously  referred  to;  and  the  admirable 
memoir  by  Professor  Plantamour,*  in  which  he  discusses  the  results  derived 
from  the  mean  of  the  ten  years  from  1841  to  1850,  has  been  more  fre- 
quently quoted  than  any  similar  paper  in  the  recent  history  of  the  barom- 
eter. Ten  years  was  a  period  long  enough  to  eliminate  nearly  if  not  quite 
all  the  anomalies  which  might  manifest  themselves  in  any  single  year,  and 
to  give  an  excellent  mean  value  for  the  computed  heights  in  each  month. 
In  spite  of  all  precautions  and  of  the  use  of  a  special  humidity  correction 
the  change  from  month  to  month  proves  to  be  nearly  as  great  as  when 

*  Memoires  de  la  Societe  de  Physique  et  d'Histoire  Naturelle  de  Geneve,  Tom.  XIII.,  1852, 
pp.  1  -  62. 


WORK  OUTSIDE  OF  CALIFORNIA.  61 

the  calculations  are  made  according  to  the  original  formula  of  Laplace. 
Plantamour's  suspicions,  as  those  of  nearly  all  previous  observers,  fell 
upon  the  method  employed  for  getting  the  mean  temperature,  and  he 
says  that  the  largest  part  of  the  discrepancies  in  barometric  measurements 
is  chargeable  to  the  assumption  "  that  the  mean  temperature  of  the  air- 
column  between  the  two  stations  is  equal  to  the  half-sum  of  the  tem- 
peratures at  the  two  extremities."  The  proper  step  to  take,  therefore,  is 
to  apply  some  correction  to  the  temperature,  determined  in  the  ordinary 
way,  so  as  to  make  it  approximate  more  closely  to  the  truth ;  for  the  true 
mean  "is  equal  to  the  half-sum  of  the  temperatures  observed  at  the  two 
extremities,  plus  a  certain  correction,  which  varies  with  the  hour  of  the 
day,  with  the  season  of  the  year,  and  from  accidental  causes." 

To  ascertain  the  value  of  this  correction,  Plantamour  reversed  the  com- 
putations for  altitude,  and,  taking  the  heights  of  the  barometers  and  the 
true  difference  of  altitude  as  the  known  quantities,  regarded  the  tempera- 
ture correction,  or  the  true  mean  temperature,  as  the  quantity  to  be  deter- 
mined. Having  in  this  way  found  what  he  considered  to  be  the  true 
temperature  of  the  mass  of  air  for  the  different  hours  of  the  day  in  each 
month,  it  required  only  a  simple  subtraction  to  know  what  correction 
ought  to  have  been  applied  to  the  observed  temperatures  at  each  hour,  to 
bring  them  into  accord  with  the  true  temperature.  These  corrections  he 
arranged  in  a  tabular  form,  and  showed  that  they  varied  less  from  month 
to  month  than  from  hour  to  hour  in  the  same  month.  The  least  values 
of  the  correction  for  the  mean  of  the  day  are  found  in  March  and  Sep- 
tember, which  months  are  accordingly  recommended  as  best  suited  for 
measuring  altitudes  barometrically.  In  July  the  altitudes  are  too  high, 
excepting  between  midnight  and  four  o'clock  in  the  morning,  and  in 
December  they  are  all  too  low,  without  exception. 

By  multiplying  each  number  in  Plantamour's  table  by  a  constant  quan- 
tity, equal  to  the  increase  in  the  computed  heights  caused  by  an  increase 
of  one  degree  in  the  assumed  value  of  the  mean  temperature,  a  table  sim- 
ilar in  form  to  Tables  XX.  -  XXII.  of  the  California  series  can  be  prepared. 
Such  a  table  has,  in  fact,  been  made,  and  was  included  by  Guyot  *  in  his 


*  Tables,  Meteorological  and  Physical,  prepared  for  the  Smithsonian  Institution,  Washington, 
1859,  Series  D,  p.  82. 


G2  BAROMETRIC  IIYPSOMETRY. 

collection.  It  would  be  easy  to  translate  this  into  English  measures,  and 
find  how  much  the  correction  for  each  thousand  feet  would  amount  to, 
but  no  practical  gain  would  ensue,  for  the  table,  even  in  that  form,  would 
not  be  adapted  for  use  in  California. 

The  same  set  of  observations  were  also  studied  independently  by  Lieu- 
tenant H.  L.  Eenny,  during  a  residence  in  Switzerland  in  1857 ;  and  a 
very  valuable  memoir,  entitled  "  On  the  Constants  of  the  Barometric  For- 
mulae which  make  correct  allowance  for  the  Hygrometric  State  of  the 
Atmosphere,"  although  by  far  the  larger  part  of  the  paper  is  taken  up 
with  the  discussion  of  the  subject  of  the  horary  correction,  was  read  by 
him  before  the  Irish  Academy  in  the  following  year.*  Plantamour's  table 
of  corrections,  above  referred  to,  is  shown  by  Eenny  to  be  defective,  because 
the  correct  height  of  the  Convent  of  Saint  Bernard  above  the  Observatory 
of  Geneva,  determined  by  an  accurate  survey  with  the  spirit-level,  was 
not  known  until  after  the  table  had  been  published.  Eenny's  own  table 
of  horary  corrections  is  more  complete  than  that  of  Plantamour,  and  was 
prepared  in  almost  precisely  the  same  way  as  that  chosen  for  the  Califor- 
nia investigation,  f  He  says :  "  I  made  no  less  than  two  hundred  and 
eighty-eight  distinct  calculations  for  every  hour,  night  and  day,  of  every 
month  of  the  year.  ....  Then  subtracting  each  calculated  height  from 
the  true  height,  as  ascertained  by  accurate  spirit-levelling,  ....  the  error 
of  each  calculated  height  is  known.  Such  error,  being  divided  by  the 
calculated  height,  gives  the  horary  correction ;  for  if  such  horary  correction 
be  multiplied  by  the  calculated  height,  we  necessarily  have  the  difference 
of  calculated  and  true  height ;  and  such  difference,  being  added  to  or  sub- 
tracted from  the  calculated  height,  according  to  the  sign  of  the  horary 
correction,  necessarily  gives  the  true  height." 

The  table  given  by  Eenny  is  arranged  in  a  different  form  from  that 


*  Transactions  of  the  Royal  Irish  Academy,  Vol.  XXIII.,  1859,  pp.  623-668. 

+  Lieutenant  Kenny's  treatment  of  the  subject  of  special  barometric  corrections  came  near 
being  overlooked  entirely  in  the  search  made  for  memoirs  of  this  character,  on  account  of  the 
incomplete  title  of  his  paper.  The  use  of  any  formula  involving  a  separate  correction  for  mois- 
ture having  been  found  impracticable  upon  the  California  work,  the  paper  of  Kenny's  was  not 
read  until  some  time  in  April,  1874,  after  all  the  tables  prepared  for  California  had  been  finished 
and  electrotyped,  and  it  was  then  examined  without  the  expectation  of  finding  anything  which 
bore  upon  the  immediate  subject  in  hand. 


WORK  OUTSIDE  OF  CALIFORNIA. 


63 


adopted  in  this  work,  and  supplies  a  correction  for  every  hour,  day  and 
night,  for  every  month  of  the  year.  A  portion  of  that  table,  so  trans- 
formed as  to  be  directly  comparable  with  Table  XXIV.  and  comprising 
only  the  hours  from  7  A.  M.  to  9  P.  M.,  is  given  below.  The  mean  of 
twenty-four  hours  has  been  given  in  preference  to  the  mean  of  the  morn- 
ing, midday,  and  evening  correction,  which  would  be  in  some  respects 
better  for  purposes  of  comparison. 


CORRECTIONS  TO   BE  APPLIED   FOR  EACH   THOUSAND   FEET  BETWEEN   GENEVA 

AND   SAINT   BERNARD. 


Hour. 

Jan. 

Feb. 

Mar. 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

7  A.M. 

+8.7 

+8.4 

+   5.6 

+  1.3 

-  0.8 

-  1.8 

-   2.0 

+  0.6 

+4.5 

+6.5 

+  10.1 

+12.5 

8    " 

+7.3 

+6.2 

+  1.7 

-  2.5 

-  4.8 

-  5.5 

-  5.9 

-  3.5 

+0.8 

+3.7 

+  8.2 

+11.2 

9    " 

+5.5 

+3.2 

-  2.3 

-  6.5 

-  8.4 

-  8.8 

-  9.3 

-  7.2 

-2.6 

+0.9 

+  5.8 

+  9.5 

10    " 

+3.5 

+0.2 

-  5.8 

-  9.7 

-11.4 

-11.3 

-11.9 

-  9.8 

-5.4 

-1.7 

+  3.4 

+  7.5 

11     « 

+2.0 

-2.4 

-  8.4 

-11.9 

-13.1 

-13.2 

-13.8 

-11.6 

-7.5 

-3.6 

+  1.5 

+  5.6 

12  M. 

+0.4 

-4.1 

-  9.7 

-12.9 

-13.8 

-14.1 

-14.6 

-12.4 

-8.4 

-4.5 

+  0.1 

+  4.3 

1  P.M. 

0 

-4.6 

-10.0 

-12.9 

-13.5 

-14.3 

-14.8 

-12.5 

-8.6 

-4.7 

-  0.4 

+  3.8 

2     ' 

+0.4 

-4.0 

-  9.0 

-11.6 

-12.4 

-13.8 

-14.2 

-11.8 

-7.9 

-4.0 

+  0.4 

+  4.2 

3    ' 

+1.4 

-2.5 

-  7.0 

-  9.8 

-10.7 

-12.6 

-12.8 

-10.6 

-6.5 

-2.6 

+   1.7 

+  5.3 

4    ' 

+2.7 

-0.5 

-  4.6 

-  7.2 

-  8.6 

-10.8 

-11.1 

-  8.9 

-4.7 

-0.9 

+  3.3 

+  6.8 

5    ' 

+4.7 

+1.8 

-  2.0 

-  4.7 

-  5.8 

-  8.3 

-  8.6 

-  6.7 

-2.6 

+1.0+  5.0 

+  8.3 

6    ' 

+6.1 

+3.7 

+  0.3 

-  2.2 

-  3.3 

-  5.6 

-  6.1 

-  4.3 

-0.6 

+2.9 

+  6.3 

+  9.7 

7    ' 

+7.0 

+5.3 

+  2.4 

-  0.1 

-  0.6 

-  2.8 

-  3.6 

-  2.0 

+1.3 

+4.6 

+  7.4 

+10.7 

8    ' 

+7.6 

+6.3 

+  4.1 

+  1.7 

+  1.7 

-  0.3 

-  1.1 

0 

+2.8 

+6.1 

+  8.1 

+11.1 

9    ' 

+7.8 

+7.1 

+  5.3 

+  3.2 

+  3.6 

+  2.1 

+  0.8 

+  1.7 

+4.0 

+7.4 

+  8.5 

+11.2 

Mean  of 

+6.2 

+4.7 

+  2.0 

-  0.8 

-  1.2 

-  2.5 

-  3.3 

-  1.4 

+  1.3 

+4.3 

+  6.9 

+  9.6 

24  Hours. 

Table  XXIV.  has  been  chosen  for  comparison  with  the  table  of  Renny, 
because  the  true  difference  of  altitude  in  the  two  cases  is  nearly  the  same. 
When  the  tables  are  laid  side  by  side,  the  first  fact  noticed  is  that  the 
corrections  for  Switzerland  are  almost  universally  smaller  numerically, 
whether  positive  or  negative,  than  they  are  for  California.  This  fact  is 
evidently  due  in  part  to  the  use  by  Renny  of  a  formula  containing  a 
special  vapor  correction,  the  effect  of  which  is,  as  has  been  shown  in 
Chapter  I.,  to  reduce  the  discrepancy  between  summer  and  winter  meas- 
urements. But  much  more  is  doubtless  due  to  climatic  differences,  and 
this  table  is  heartily  welcomed  as  a  strong  piece  of  evidence  in  confirma- 


64  BAROMETKIC   HYPSOMETRY. 

tion  of  the  view  held,  even  before  the  investigation  in  California  was 
begun,  that,  in  order  to  attain  to  the  best  results  the  world  over,  it  will 
be  necessary  to  have  similar  tables  prepared  for  each  mountain  region, 
especially  if  the  peculiarities  'of  climate  are  so  marked  as  they  are  on  the 
Pacific  coast  of  the  United  States. 

Setting  aside  the  numerical  values  of  the  corrections,  the  general  features 
of  the  two  tables  are  wonderfully  alike.  There  is  a  regular  gradation  in 
both  cases,  from  morning  to  midday  and  thence  to  evening;  though  the 
turning-point  in  California  is  from  one  to  two  hours  later  than  in  Switzer- 
land. If  the  corrections  for  the  separate  hours  through  the  several 
months  are  compared  with  each  other  along  the  horizontal  lines  of  the 
tables,  a  similar  diminution  in  value  from  January  to  spring  and  summer, 
and  a  corresponding  rise  in  the  latter  part  of  the  year,  are  observed.  The 
minimum  values,  however,  do  not  occur  in  the  same  mouths  in  both  cases, 
particularly  for  the  early  morning  and  late  evening  hours.  The  higher 
latitude  of  Geneva,  and  the  consequent  difference  in  the  times  of  sunrise 
and  sunset,  may  possibly  have  some  influence  in  this  respect. 

When  the  separate  columns  are  compared  in  order  to  see  at  what  hours 
a  change  in  the  sign  of  the  correction  occurs,  the  coincidence  is  not  abso- 
lute, but  closer  than  might  be  expected.  In  neither  table  is  there  a 
negative  correction  for  January  or  December.  From  February  to  June 
the  afternoon  change  from  minus  to  plus  takes  place,  either  at  the  same 
hour  or  at  points  only  one  hour  apart  in  the  two  tables.  For  the  fore- 
noons the  positive  sign  prevails  in  California  to  a  later  hour  as  a  rule,  but 
with  numerically  small  values.  The  hours  which  give  the  closest  approx- 
imation to  the  truth  in  the  several  months  agree  for  some  seasons  but 
differ  for  others,  which  is  not  at  all  surprising,  when  the  local  peculiarities 
of  the  two  countries  are  taken  into  account. 

In  a  second  table  Kenny  entered  side  by  side  with  the  horary  correc- 
tions the  half-sum  of  the  temperatures  observed  at  the  extreme  stations, 
and  thus  showed  that  the  connections  between  the  greatest  errors,  whether 
in  excess  or  defect,  and  the  maximum  or  minimum  of  temperature  was 
not  so  uniform  as  had  been  supposed,  particularly  for  the  night  hours; 
during  the  day  there  was  seldom  more  than  one  hour's  difference  between 
the  two  critical  points. 

In  applying  his   table  of  corrections   to  the   observations  of  the   year 


WORK  OUTSIDE  OF  CALIFORNIA.  65 

1855,  Eenny  was  disappointed  at  finding  that,  when  he  calculated  the 
difference  of  altitude  between  Geneva  and  St.  Bernard  for  those  hours  in 
each  month  at  which  the  horary  correction  in  his  table  was  zero,  he  ob- 
tained results  which  did  not  agree  exactly  with  the  truth.  That  this 
should  be  so  is  evident,  when  it  is  recollected  that  mean  results  derived 
from  observations  running  through  a  period  of  ten  or  more  years  would 
naturally  differ  in  some  respects  from  similar  results  based  upon  a  shorter 
period.  The  practical  conclusion  drawn  by  Kenny  from  this  apparent 
failure  of  his  cherished  table  was  "  that,  although  the  Table  of  Horary  Cor- 
rections meet  not  our  wishes,  nor  even  our  expectations,  it  diminishes  (by 
one  half)  the  errors  of  the  other  formulae.  Therefore  let  us  not  despond, 
• — all  we  desire  has  not  been  realized,  but  considerable  improvement  has 
been  made,  and  by  diligence  and  zeal  more  may  hereafter  be  done." 

A  portion  of  his  concluding  remarks  presents  with  so  much  force  the 
argument  for  the  prosecution  of  work  of  this  kind,  and  expresses  so  exactly 
the  belief  which  prompted  and  sustained  the  investigation  in  California, 
that  space  is  taken  for  an  additional  quotation.  After  speaking  of  the 
possible  future  improvements  in  the  constants  of  the  formula,  he  says : 
"  Small  indeed  will  be  such  improvements  compared  to  those  which  will 
result  from  the  employment  of  correct  tables  of  horary  correction,  or  from 
a  more  correct  method  than  the  present  one  of  estimating  the  mean  tem- 
perature of  the  atmospheric  column  between  the  stations  of  barometric 
observations.  To  these  particular  objects  all  attention  ought  now  to  be 
directed,  for  here  at  present  is  the  weak  side  of  barometric  levelling.  To 
obtain  these  objects,  too  many  hands  cannot  be  employed  in  making 
observations,  ....  the  results  of  which,  being  compared  with  heights 
accurately  determined  by  spirit-levelling,  may  furnish  data  for  such  pur- 
pose  But  we  are  warned  by  the  facts  of  this  paper,  that  with  even 

the  assistance  of  a  sound  table  of  local  horary  corrections,  we  are  not  to 
expect  exemption  from  serious  error  on  all  occasions." 

The  brothers  Schlagintweit,  while  engaged  in  the  service  of  the  East 
India  Company,  from  the  year  1854  to  1858,  made  a  praiseworthy  attempt 
to  apply  systematic  corrections  for  the  daily  and  yearly  variation  to  their 
barometric  measurements;  but  the  observations  upon  which  they  had  to 
rely  were  too  few  in  number  to  establish  the  values  of  the  corrections 
beyond  question.  From  their  account  it  appears  that  the  monthly  means 


66  BAROMETRIC   HYPSOMETRY. 

of  observations  at  four  corresponding  pairs  of  stations  were  computed  as 
a  basis  for  the  annual  variation,  the  true  difference  of  altitude  being  sup- 
posed to  be  known,  either  by  the  trigonometrical  method,  or  from  the 
mean  of  a  year's  observations  with  the  barometer.* 

The  annual  variation  in  India  does  not  follow  so  simple  a  law  as  it 
does  in  California.  In  each  one  of  the  four  cases  the  existence  of  two 
maxima  and  two  minima  instead  of  one  was  quite  clearly  indicated ; 
an  explanation  for  which  was  sought  in  certain  peculiar  climatic  condi- 
tions prevailing  at  the  months  of  transition  from  the  wet  to  the  dry,  or 
from  the  dry  to  the  wet  season.  It  seems  reasonable,  however,  to  doubt 
the  adequacy  of  the  explanation,  and,  in  view  of  the  anomalies  exposed 
to  view  in  the  investigation  in  California,  to  hold  to  the  belief  that  if 
more  extensive  series  of  observations  could  have  been  obtained  in  India, 
the  variation  from  month  to  month  would  have  been  much  more  uni- 
form. 

The  corrections  for  the  hour  of  the  day  were  computed  independently, 
and  were  understood  to  be  the  quantities  by  which  the  results  of  com- 
putation were  to  be  increased  or  diminished  in  order  to  make  them  agree, 
not  with  the  annual  or  corrected  mean,  but  with  the  monthly  mean.  To 
obtain  the  final  result  there  wras  still  to  be  added  or  subtracted  the  cor- 
rection for  the  particular  month  in  question.  The  observations  from  which 
the  daily  variation  was  deduced  seem  not  to  have  been  continued  for  any 
great  length  of  time  at  any  one  place,  it  being  perhaps  thought  that  the 
amount  of  change  from  hour  to  hour  would  be  the  same  whatever  the 

O 

season  of  the  year. 

In  their  table  of  periodic  corrections  the  Messrs.  Schlagintweit  have  also 
recognized  the  fact  that  the  corrections  per  hundred  or  per  thousand  feet 
are  greater  when  the  differences  of  altitude  are  small  than  when  they  are 
large,  and  have  given  three  series,  calculated  for  differences  of  400,  1,000, 
and  1,600  feet  respectively.  For  greater  altitudes  the  relative  correction 
was  considered  the  same  as  for  1,600  feet.  Whether  this  is  strictly  the 
case  or  not,  it  is  evident  that  the  hypsometric  results  obtained  by  these 
explorers  in  India  are  entitled  to  more  than  a  common  measure  of  coiifi- 


*  Results  of  a  Scientific  Mission  to  India  and  High  Asia.     Leipzig  and  London,  1862,  Vol.  II. 
pp.  47-64. 


WORK  OUTSIDE  OF  CALIFORNIA.  67 

dence.  The  observations  were  doubtless  taken  with  care,  the  use  of  a 
plumb-line  even  being  recommended  in  order  to  secure  the  verticality  of 
the  barometer,  and  to  the  computations  there  was  certainly  applied  every 
known  correction  by  which  a  closer  approximation  to  the  truth  would  be 
reached. 

The  division  of  the  periodic  correction  into  two  parts,  one  for  the  month 
and  one  for  the  hour  of  the  day,  seems  to  be  an  unnecessary,  if  not  a  false 
step.  The  California  tables  cannot,  indeed,  be  cited  in  proof  either  of  this 
or  the  contrary  statement  with  much  effect,  because  of  the  lack  of  hourly 
observations,  and,  for  the  present,  the  question  will  have  to  be  left  un- 
settled. 

The  subject  of  the  daily  period  in  barometric  measurements  has  also 
been  investigated  in  minute  detail  by  Professor  Bauernfeind  of  Munich. 
In  August,  1857,  with  the  assistance  of  eleven  students,  he  determined  by 
spirit-level  the  height  of  the  top  of  the  Grosser  Miesing  and  of  three 
intermediate  stations  above  the  plain.  The  difference  of  level  between  the 
extreme  stations  was  about  3,650  feet.  Half-hourly  observations  of  the 
barometer,  thermometer,  psychrometer,  and  the  direction  of  the  wind,  were 
taken,  with  some  omissions,  from  eight  in  the  morning  to  six  in  the  even- 
ing, between  the  twentieth  and  twenty-eighth  of  the  same  month.  These 
observations  were  subjected  to  a  thorough  analysis  in  all  respects,  and 
the  results  published  in  1862.  The  portion  relating  to  the  accuracy  of 
the  measurements  is  all  that  will  be  referred  to  at  this  time.* 

The  computed  differences  of  altitude  when  arranged  in  a  tabular  form 
showed  "  in  a  surprising  manner  "  that  the  results  were  too  high  between 
ten  o'clock  in  the  morning  and  four  in  the  afternoon,  but  too  low  at 
earlier  or  later  hours.  The  obvious  relation  existing  between  the  com- 
puted heights  and  the  daily  increase  and  decrease  of  the  observed  tem- 
peratures was  the  first  subject  for  examination.  There  being  no  reason  to 
distrust  the  correctness  of  the  formulae  employed  in  the  computation,  the 
source  of  error  had  to  be  looked  for  in  the  observations  themselves.  If 
these  observations  gave  the  mean  temperature  correctly,  there  was  no 
reason  why  the  formula  should  not  give  the  difference  of  altitude  cor- 

*  Beobachtungen  und  Untersuchungen  iiber  die  Genauigkeit  barometrischer  Hbhenmessungen, 
etc.,  Miinchen,  1862,  pp.  59-84. 


68  BAROMETRIC   HYPSOMETRY. 

rectly ;  consequently  the  conclusion  was  reached  by  Bauernfeind,  as  by  so 
many  others,  that  the  stratum  of  air  nearest  the  surface  of  the  earth  is  so 
affected  by  radiation  that  the .  thermometers  at  the  extreme  stations  do  not 
give  the  true  mean  temperature  except  at  certain  hours  of  the  day.  These 
hours,  according  to  his  observations,  are  ten  in  the  morning  and  four  in 
the  afternoon.  For  other  hours  of  the  day  the  observations  for  tempera- 
ture are  wrong  and  must  be  corrected.  This  view  of  the  subject  is  essen- 
tially the  same  as  that  taken  by  Plantamour;  but  a  different  method  of 
obtaining  the  value  of  the  correction  was  chosen. 

Bauernfeind  represented  the  deviation  of  the  computed  from  the  true 
height  by  a  formula  of  the  same  general  character  as  that  used  by 
Kaemtz*  in  his  investigations  at  the  Eighi  and  Faulhorn,  and  then  sub- 
stituted in  place  of  this  formula,  for  the  sake  of  simplicity  in  the  numeri- 
cal work,  the  equations  of  two  common  parabolas,  one  of  which  coincided 
almost  exactly  with  that  part  of  the  actual  curve  which  represented  the 
changes  in  the  forenoon,  and  the  other  with  the  remainder.  With  the 
aid  of  these  equations  he  computed  a  table  of  corrections  in  degrees  to  be 
applied  to  the  observed  temperatures  in  order  to  get  the  real  mean  tem- 
perature of  the  air-column  between  the  two  barometers  at  different  hours 
of  the  day  from  eight  o'clock  until  six.  No  attempt  was  made  to  extend 
the  discussion  over  the  hours  of  the  night  on  account  of  the  lack  of 
observations. 

A  recomputation  of  the  differences  of  altitude  with  the  corrected  tem- 
peratures failed  to  give  absolutely  correct  results  in  all  cases,  but  the 
amount  of  error  was  slight  and  its  periodicity  disappeared  entirely,  the 
variations  being  fairly  chargeable  to  unavoidable  errors  of  observation. 

The  inapplicability  of  his  table  of  corrections  for  other  localities  was 
clearly  recognized  by  Bauernfeind,  for  he  says  that,  as  soon  as  the  tem- 
perature correction  which  he  determined  for  a  particular  place  and  season 
could  be  extended  by  long-continued  observations  over  other  months  and 
other  regions,  "we  shall  be  able  to  make  barometric  measurements  at 
every  hour  from  morning  to  evening  with  almost  the  same  degree  of 
accuracy  as  we  can  now  at  ten  in  the  morning  and  four  in  the  after- 
noon." It  does  not  appear  from  anything  published  in  this  connection  that 

*  See  page  59. 


WORK  OUTSIDE   OF  CALIFORNIA.  69 

Bauernfeind's  attention  had  been  called  to  the  annual  variation,  or  the 
effects  of  the  different  seasons  of  the  year,  any  further  than  to  raise  a 
suspicion  that  the  numerical  values  of  the  corrections  would  vary  from 
month  to  month,  without  any  change  in  the  hours  at  which  the  correction 
is  zero. 

Having  treated  of  the  effects  of  radiation  upon  the  temperature  of  the 
stratum  of  air  in  contact  with  the  earth,  he  next  undertook  the  discussion 
of  the  absolute  and  relative  effects  of  other  possible  errors  of  observation, 
such  as  the  incorrect  reading  of  the  attached  thermometer,  or  of  the  true 
height  of  the  mercury  in  the  barometer  at  either  station.  This  discussion 
was  searching  and  valuable  in  itself,  but  developed  no  new  explanation 
for  the  observed  variations.  In  fact,  it  may  be  said  to  have  strengthened 
the  view  that,  provided  the  temperature  term  can  be  determined  with 
accuracy,  the  other  incidental  errors  are  of  comparatively  little  importance 
when  the  instruments  are  in  good  order  and  the  observations  are  properly 
made. 

It  was  the  daily  period,  again,  which  Dr.  Eiihlmann,  while  yet  a  student 
at  Dresden,  in  1864,  undertook  to  investigate.  He  was  acquainted  with 
Bauernfeind's  work,  and  hoped  to  contribute  something  additional  by  his 
own  labors.  The  point  selected  by  him  for  his  observations  was  the  Val- 
tenberg,  near  Bischofswerda  in  Saxony,  the  height  of  which  he  determined 
by  spirit-level  to  be  869  feet.  His  observations  were  continued  for  about 
six  weeks  in  the  months  of  August  and  September,  1864,  and  yielded  such 
results  that  he  was  induced  to  enter  upon  a  critical  examination  of  the 
records  of  the  meteorological  stations  of  Geneva  and  St.  Bernard,  so  far  as 
they  were  accessible  to  him.  The  observations  of  which  he  made  the 
principal  use  were  those  of  the  six  years  from  1860  to  1866.  This 
examination  carried  him  considerably  beyond  the  limits  originally  pro- 
posed, and  his  published  book  treats  largely  of  the  history  of  the  barometer 
and  its  use  in  practical  meteorology  by  aiding  in  the  solution  of  problems 
relating  to  the  physics  of  the  atmosphere.* 

Eiihlmann's  summary  of  the  results  of  his  study  of  the  errors  to  which 

*  Die  barometrischen  Hbhenmessungen,  Leipzig,  1870.  The  opportunity  is  here  taken  to 
acknowledge  the  debt  of  thanks  which  is  due  to  Dr.  Ruhlmann,  particularly  for  the  valuable  list 
of  titles  of  books  and  memoirs  relating  to  the  barometer  and  its  applications.  Without  this  aid 
the  labor  of  preparing  the  present  chapter  would  have  been  increased  many  fold. 


70  BAROMETRIC  HYPSOMETRY. 

the  barometric  method   of  measuring   altitudes  is   liable  is  comprised  in 
four  paragraphs,  as  follows :  — 

"  I.  Heights  computed  from  barometric  and  thermometric  observations 
are  in  general  essentially  greater  by  day  than  by  night;  they  show  a 
decided  daily  period. 

"  II.  Heights  computed  from  daily  and  monthly  means  of  meteorological 
observations  show  a  yearly  period.  They  are  too  small  in  winter  and  too 
great  in  summer.  The  amplitude  of  the  yearly  period,  however,  is  less 
than  that  of  the  daily. 

"III.  Yearly  means  of  meteorological  observations  give  heights  which 
differ  but  little  from  the  true  values. 

"IV.  The  periodicity  of  barometric  measurements,  both  the  daily  and 
the  yearly,  is  made  up  of  two  parts,  one  of  which,  by  far  the  larger,  arises 
from  variations  in  temperature,  and  the  other,  the  smaller,  from  variations 
in  the  barometer.  These  two  parts  have,  in  general,  opposite  signs." 

The  establishment  of  these  four  propositions  and  the  discussion  of  their 
causes  were  the  principal  features  of  the  problem  as  undertaken  by 
Eiihlmann.  For  the  cause  of  both  the  daily  and  the  yearly  periodicity 
he  looked  particularly  to  the  temperature  term,  after  having  become  satis- 
fied that  there  were  no  sources  of  error  in  the  other  parts  of  the  formula 
which  could  account  for  discrepancies  so  great  in  amount.  The  conclu- 
sions reached  were  that  the  half-sum  of  the  temperatures  at  the  extreme 
stations  does  not  give  the  real  mean  temperature  of  the  column  of  air, 
and,  as  a  necessary  consequence  of  this,  that  the  true  temperature  of  the 
air-column  changes,  during  any  given  period  of  time,  neither  so  much 
nor  so  rapidly  as  the  arithmetical  mean  of  the  temperatures  observed  at 
the  upper  and  lower  stations.  By  reversing  the  computations  and  con- 
sidering, as  Plantamour  did,  the  true  temperature  to  be  the  unknown 
quantity,  he  obtained  mean  values  of  the  temperature  for  every  two  hours 
in  the  month  of  July ;  this  month  being  selected  because  it  was  the  01 
which  showed  the  greatest  amplitude  in  the  daily  period.  The  results 
showed  that  while  between  four  in  the  morning  and  two  in  the  afternoon 
there  was,  on  the  average,  a  variation  of  16°.  5  F.  at  Geneva,  and  of  11°  F. 
at  St.  Bernard,  the  variation  in  the  true  temperature  of  the  air-column 
amounted  to  only  4°.5  F.,  the  minimum  occurring  at  six  in  the  morning 
and  the  maximum  at  six  in  the  evening.  Similar  computations  for  the 


WORK  OUTSIDE   OF  CALIFORNIA.  71 

other  months  led  to  similar,  though  numerically  smaller  results.  In  De- 
cember, for  instance,  the  range  was  5°.2  at  Geneva,  and  3°.2  at  St.  Ber- 
nard, but  only  1°.3  F.  for  the  true  temperature  of  the  air  between  the 
two  stations. 

When  the  monthly  means  of  recorded  temperatures  were  compared  in 
a  similar  way  with  the  true  mean  temperatures  of  the  air-column  in  the 
several  months,  it  was  found  that  the  range  from  summer  to  winter  at 
Geneva  amounted  to  32°.8  R,  and  at  St.  Bernard  to  28°.2  F.,  although  the 
range  of  the  true  mean  was  only  24°6  F.  From  such  results  as  these  it 
was  evident  that  the  mass  of  air  included  between  two  stations  does  not 
become  heated  so  much  nor  so  rapidly  as  is  indicated  by  thermometers 
near  the  earth's  surface;  that  the  mass  of  air  shares  to  only  a  slight 
degree  the  daily  variations  at  the  surface  ;  and  that  it  changes  in  temper- 
ature from  month  to  month  as  a  whole  at  a  considerably  less  rapid  rate 
than  do  the  strata  in  contact  with  the  surface.  The  conclusion  is  there- 
fore inevitable  that  "  the  thermometers  at  the  meteorological  stations  do 
not  give  the  true  temperature  of  the  intervening  air-column,  but  some 
other  quantity,"  which  stands  in  no  simple  relation  to  the  true  temperature. 

One  of  the  practical  results  of  Riihlmann's  labors  for  hypsometrical 
purposes  is  the  following  statement  of  the  hours  of  the  day  at  which  the 
best  approximation  to  the  true  differences  of  height  will  be  attained  :  — 


In 

January        

12 

M. 

« 

February  

10 

A.M. 

and 

4 

P.M. 

« 

March  ........ 

8 

It 

U 

<; 

U 

« 

April        ....... 

7 

t( 

a 

7 

tl 

M 

May    

7 

tt 

a 

7 

It 

« 

6 

u 

n 

9 

It 

« 

July    

6 

it 

u 

9 

tl 

•  « 

August    

7 

u 

tt 

8 

U 

(4 

September  

8 

n 

it 

0 

tt 

i. 

October  

10 

it 

it 

4 

tt 

U 

November  ....... 

11 

tt 

n 

2 

It 

U 

December      

m 

. 

1 

tt 

No  table  of  corrections  to  be  applied  to  observations  taken  at  different 
hours  is  given;  and  thus  the  work  of  Eiihlmann,  valuable  as  it  is  in  all 
respects,  falls  short  of  reaching  the  point  of  practical  applicability  which 


72  BAROMETRIC  HYPSOMETRY. 

was  aimed  at  in  the  California  investigation.  The  method  proposed  by 
him  for  finding  the  true  mean  temperature  of  the  air  between  two  stations 
is  too  complicated  for  ordinary  use,  and  requires  more  labor  than  the 
improved  degree  of  accuracy*  obtained  would  justify. 

From  the  foregoing  resume  it  is  evident  that  the  existence  of  a  double 
periodicity  in  barometric  measurements  has  attracted  the  attention  of  ob- 
servers for  nearly  three  quarters  of  a  century,  but  that  in  almost  no  instance 
has  any  one  pursued  the  subject  far  enough  to  be  able  to  state,  with  much 
approach  to  accuracy,  the  probable  error  of  measurements  made  under 
different  circumstances.  It  is  to  this  failure  to  reach  practical  results 
that  the  comparative  obscurity  into  which  these  investigations  appear  to 
have  fallen  must  be  ascribed.  One  of  the  most  striking  facts  noticed  in 
the  history  of  this  subject  is  that,  almost  without  exception,  each  new 
investigator  entered  upon  what  he  thought  an  untrodden  field,  entirely 
ignorant  of  the  labors  of  his  predecessors,  and  sought  by  independent  and 
original  work  to  remedy  or  account  for  difficulties  which  had  arisen  in 
his  own  experience. 

A  long  step  is  taken  when  the  months  and  hours  can  be  given  at 
which  the  errors  may  be  expected  to  be  least;  and  when  the  determina- 
tion of  the  altitudes  of  a  few  prominent  points  only  is  undertaken,  it 
may  well  be  advisable  to  select  the  most  favorable  time  for  the  observa- 
tions. But  upon  extensive  surveys,  when  a  large  tract  of  country  has  to 
be  examined  in  a  short  time,  and  barometric  observations  have  to  be 
taken  at  several  points  in  the  course  of  a  single  day,  it  becomes  necessary 
to  take  at  least  one  step  additional.  What  that  step  shall  be  may  still 
be  thought  by  some  an  open  question  ;  but  the  choice  will  have  to  lie 
between  a  change  of  the  observed  reading  of  the  instruments  at  the  two 
corresponding  stations,  and  the  application  of  a  correction  to  the  com- 
puted results.  The  latter  course,  which  recommends  itself  by  its  greater 
simplicity  and  equal  accuracy,  is  the  one  which  seems  most  likely  to  give 
good  results  for  California  and  the  Pacific  coast. 


TABLES, 


I. 


SACKAMENTO   AND  COLFAX.    CFrasi  YEAE.) 


By  Railroad  Survey,  2399  feet. 


Date. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

1870  October 

2357.9 

—41.1 

2457.4 

+58.4 

2370.0 

—29.0 

2393.4 

—  5.6 

November 

2353.9 

—45.1 

2435.6 

+36.6 

2368.6 

—30.4 

2386.5 

—12.5 

December 

2357.8 

—41.2 

2435.2 

+36.2 

2374.5 

—24.5 

2389.5 

—  9.5 

1871  January 

2353.0 

—46.0 

2425.3 

+26.3 

2362.7 

—36.3 

2380.2 

—18.8 

February 

2372.1 

—26.9 

2432.4 

+33.4 

2405.5 

+  6.5 

2402.8 

+  3.8 

March 

2388.3 

-10.7 

2455.2 

+56.2 

2395.8 

—  3.2 

2412.9 

+13.9 

April 

2385.8 

—13.2 

2459.9 

+60.9 

2387.4 

—11.6 

2410.6 

+11.6 

May 

2419.1 

+20.1 

2477.8 

+78.8 

2411.6 

+12.6 

2435.6 

+36.6 

June 

2410.8 

+11.8 

2493.6 

+94.6 

2386.7 

—12.3 

2430.3 

+31.3 

July 

2416.9 

-4-17.9 

2490.1 

+91.1 

2399.1 

+  0.1 

2435.5 

+36.5 

August 

2402.8 

+  3.8 

2490.7 

+91.7 

2379.5 

—19.5 

2424.9 

+25.9 

September 

2377.9 

—21.1 

2479.5 

+80.5 

2371.9 

-27.1 

2409.6 

+10.6 

Mean  of  Year 

2383.0 

—16.0 

2461.1 

+62.1 

2384.4 

—14.6 

2409.3 

+10.3 

II. 


SACRAMENTO    AND    COLFAX.     (SECOND  YEAH.) 


By  Railroad  Sill-ivy,  2399  feet. 


Date. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

1871  October 

2360.6 

—38.4 

2471.4 

+72.4 

2365.5 

—33.5 

2398.9 

-  o.l 

November 

2360.5 

—38.5 

2439.3 

+40.3 

2371.8 

—27.2 

2389.9 

-  9.1 

December 

2379.1 

—19.9 

2421.1 

+22.1 

2404.9 

+  5.9 

2400.9 

+  1.9 

1872  January 

2371.8 

—27.2 

2425.1 

+26.1 

2388.9 

—10.1 

2395.4 

-  3.6 

February 

2383.4 

—15.6 

2421.2 

+22.2 

2387.9 

—11.1 

2397.5 

-  1.5 

March 

2402.0 

+  3.0 

2443.8 

+44.8 

2391.0 

-  8.0 

2412.4 

+13.4 

April 

2426.5 

+27.5 

2453.8 

+54.8 

2406.6 

+  7.6 

2429.2 

+30.2 

May 

2432.4 

+33.4 

2463.7 

+64.7 

2395.5 

—  3.5 

2431.1 

+32.1 

June 

2421.6 

+22.6 

2441.8 

+42.8 

2386.7 

—12.3 

2416.5 

+17.5 

July 

2441.2 

+42.2 

2481.0 

+  S2.0 

2397.8 

—  1.2 

2440.6 

+41.6 

August 

2407.1 

+  8.1 

2466.1 

+67.1 

2372.7 

—26.3 

2415.1 

+16.1 

September 

2370.7 

—28.3 

2433.1 

+34.1 

2366.2 

—32.8 

2389.3 

-  9.7 

Mean  of  Year 

2396.4 

-  2.6 

2446.8 

+47.8 

2386.3 

—12.7 

2409.7 

+10.7 

76 


TABLES  OF 


III. 

SACRAMENTO    AND    COLFAX.     (THIRD  YEAR.) 


By  Railroad  Survey,  iSgg  feet. 


Date. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

1872  October 

2353.4 

—45.6 

2429.0 

+  30.0 

2336.4 

—62.6 

2372.9 

—26.1 

November 

2380.2 

—18.8 

2433.6 

+  34.6 

2360.9 

—38.1 

2392.1 

-  6.9 

December 

2354.2 

—44.8 

2424.3 

+  25.3 

2364.1 

—34.9 

2381.2 

—17.8 

1873  January 

2362.3 

—36.7 

2445.5 

+  46.5 

2372.7 

—26.3 

2393.3 

-  5.7 

February 

2385.1 

—13.9 

2430.2 

+  31.2 

2392.3 

-  6.7 

2402.8 

+  3.8 

March 

2389.7 

—  9.3 

2470.8 

+  71.8 

2390.5 

—  8.5 

2417.3 

+18.3 

April 

2448.0 

+49.0 

2512.1 

+113.1 

2458.9 

+59.9 

2472.8 

+73.8 

May 

2447.3 

+48.3 

2494.9 

+  95.9 

2422.8 

+23.8 

2454.4 

+55.4 

June 

2457.7 

+58.7 

2535.6 

+136.6 

2432.0 

+33.0 

2474.7 

+75.7 

July 

2445.6 

+46.6 

2482.3 

+  83.3 

2426.4 

+27.4 

2451.2 

+52.2 

August 

2459.3 

+60.3 

2516.9 

+117.9 

2430.1 

+31.1 

2469.5 

+70.5 

September 

2382.5 

—16.5 

2462.4 

+  63.4 

2388.9 

—10.1 

2410.7 

+11.7 

Mean  of  Year 

2405.4 

+  6.4 

2469.8 

+  70.8 

2398.0 

-  1.0 

2424.4 

+25.4 

IV. 


SACRAMENTO    AND   SUMMIT.     (FIRST  YEAR.) 


By  Railroad  Survey,  6989  feet. 


Date. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

1870  October 

6778.4 

—210.6 

7037.7 

+  48.7 

6819.6 

—169.4 

6879.8 

—109.2 

November 

6760.5 

—228.5 

7006.9 

+  17.9 

6817.5 

—171.5 

6862.2 

—126.8 

December 

6750.7 

—238.3 

6963.5 

-  25.5 

6817.9 

—171.1 

6844.5 

—144.5 

1871  January 

6776.8 

—212.2 

6961.1 

-  27.9 

6823.4 

—165.6 

6853.9 

—135.1 

February 

6851.7 

—137.3 

7040.1 

+  51.1 

6920.6 

—  68.4 

6936.5 

—  52.5 

March 

6887.4 

—101.6 

7080.7 

+  91.7 

6915.4 

-  73.6 

6961.1 

-  27.9 

April 

6924.6 

-  64.4 

7112.6 

+123.6 

6894.4 

—  94.6 

6976.6 

-  12.4 

May 

6972.7 

-  16.3 

7134.3 

+145.3 

6921.3 

-  67.7 

7008.8 

+  19.8 

June 

6946.1 

-  42.9 

7160.1 

+171.1 

6891.4 

-  97.6 

6998.4 

+     9.4 

July 

6881.5 

—107.5 

7135.2 

+146.2 

6876.0 

—113.0 

6965.1 

—  23.9 

August 

6839.5 

—149.5 

7154.2 

+165.2 

6825.1 

—163.9 

6940.2 

-  48.8 

September 

6856.9 

—132.1 

7115.1 

+126.1 

6836.6 

—152.4 

6936.8 

—  52.2 

Mean  of  Year 

6852.2 

—136.8 

7075.1 

+  86.1 

6863.3 

—125.7 

6930.3 

—  58.7 

BAROMETRIC  ALTITUDES. 


77 


V. 


SACEAMENTO    AND    SUMMIT.     (SECOND  YEAR.) 

By  Railroad  Survey,  6989  feet. 


Date. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

1871  October 

6771.9 

—217.1 

7100.7 

+111.7 

6810.7 

—178.3 

6894.2 

—94.8 

November 

6825.8 

—163.2 

7051.4 

+  62.4 

6869.5 

—119.5 

6915.2 

—73.8 

December 

6868.8 

—120.2 

6989.6 

-f-     0.6 

6912.7 

-  76.3 

6923.0 

—66.0 

1872  January 

6848.5 

—140.5 

6964.6 

-  24.4 

6893.1 

-  95.9 

6902.2 

—86.8 

February 

6959.2 

—  29.8 

7020.1 

+  31.1 

6978.3 

-  10.7 

6985.8 

—  3.2 

March 

6929.2 

—  59.8 

7033.5 

+  44.5 

6951.5 

-  37.5 

6970.8 

—18.2 

April 

6968.1 

—  20.9 

7065.4 

+  76.4 

6961.0 

-  28.0 

6998.5 

+  9.5 

May 

6936.3 

-  52.7 

7064.9 

-f-  75.9 

6904.1 

-  84.9 

6968.3 

—20.7 

June 

6950.9 

-  38.1 

7076.0 

+  87.0 

6886.5 

—102.5 

6970.9 

—18.1 

July 

6934.9 

-  54.1 

7096.0 

+107.0 

6887.7 

—101.3 

6973.1 

—15.9 

August 

6883.2 

—105.8 

7097.3 

+108.3 

6879.9 

—109.1 

6953.2 

—35.8 

September 

6848.4 

—140.6 

7073.9 

+  84.9 

6887.3 

-101.7 

6936.4 

—52.6 

Mean  of  Year 

6893.8 

-  95.2 

7052.8 

+  63.8 

.6901.9 

-  87.1 

6949.3 

—39.7 

VI. 


SACRAMENTO    AND  SUMMIT.     (THIRD  YEAR.) 


By  Railroad  Survey,  6989  feet. 


Date. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

1872  October 

6814.2 

—174.8 

7070.0 

+  81.0 

6858.5 

—130.5 

6914.7 

-  74.3 

November 

6809.5 

—179.5 

7030.3 

+  41.3 

6829.9 

—159.1 

6889.8 

—  99.2 

December 

6799.1 

—189.9 

6976.5 

-  12.5 

6839.7 

—149.3 

6871.5 

—117.5 

1873  January 

6844.9 

—144.1 

7015.7 

+  26.7 

6884.5 

—104.5 

6914.4 

-  74.6 

February 

6961.6 

-  27.4 

7089.6 

+100.6 

6989.4 

+     0.4 

7013.3 

+  24.3 

March 

6881.4 

—107.6 

7083.5 

+  94.5 

6925.2 

-  63.8 

6963.3 

-  25.7 

April 

7002.8 

+  13.8 

7150.6 

+161.6 

7012.4 

+  23.4 

7055.7 

+  66.7 

May 

6977.7 

—  11.3 

7181.3 

+192.3 

6970.6 

-  18.4 

7042.8 

+  53.8 

June 

6969.2 

-  19.8 

7173.8 

+184.8 

6985.7 

-    3.3 

7041.9 

+  52.9 

July 

6957.2 

-  31.8 

7088.3 

+  99.3 

6983.3 

-    5.7 

7010.3 

+  21.3 

August 

6999.0 

+  10.0 

7161.7 

+172.7 

7015.0 

+  26.0 

7059.4 

+  70.4 

*  September 

6852.6 

—136.4 

7094.5 

+105.5 

G861.9 

—127.1 

6936.6 

-  52.4 

Mean  of  Year 

6905.8 

-  83.2 

7093.0 

+104.0 

6929.7 

-  59.3 

6976.1 

-  12.9 

*  Mean  of  First  and  Second  Years. 


78 


TABLES  OF 


VII. 

COLFAX   AND   SUMMIT.     (FIRST  YEAR.) 


By  Railroad  Survey,  4690  feet. 


Date. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

1870  October 

4475.4 

—114.6 

4630.7 

4-  40.7 

4493.9 

-  96.1 

4534.7 

—55.3 

November 

4471.3 

—118.7 

4614.3 

+  24.3 

4496.9 

-  93.1 

4526.9 

—63.1 

December 

4453.9 

—136.1 

4584.0 

—     6.0 

4488.9 

—101.1 

4509.4 

—80.6 

1871  January 

4483.7 

—106.3 

4606.3 

4-  16.3 

4512.1 

-  77.9 

4534.1 

—55.9 

February 

4517.4 

-  72.6 

4638,0 

+  48.0 

4538.4 

-  51.6 

4564.3 

—25.7 

March 

4541.1 

-  48.9 

4650.3 

+  60.3 

4543.5 

-  46.5 

4578.1 

—11.9 

April 

4582.3 

—    7.7 

4684.3 

4-  94.3 

4533.3 

-  56.7 

4599.8 

4-  9.8 

May 

4597.4 

+    7.4 

4690.3 

+100.3 

4535.6 

-  54.4 

4608.3 

4-18.3 

June 

4604.0 

4-  14.0 

4719.3 

4-129.3 

4555.6 

-  34.4 

4626.7 

4-36.7 

July 

4563.4 

-  26.6 

4719.6 

4-129.6 

4552.6 

-  37.4 

4612.3 

4-22.3 

August 

4540.8 

-  49.2 

4728.7 

4-138.7 

4526.3 

-  63.7 

4598.4 

4-  8.4 

September 

4530.8 

-  59.2 

4697.3 

4-107.3 

4512.0 

-  78.0 

4581.1 

—  8.9 

Mean  of  Year 

4530.1 

—  59.9 

4663.6 

4-  73.6 

4524.1 

-  65.9 

4572.8 

—17.2 

VIII. 

COLFAX    AND    SUMMIT.     (SECOND  YEAR.) 


By  Railroad  Survey,  jSgofeet. 


Date. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

1871  October 

4481.9 

—108.1 

4680.5 

4-  90.5 

4506.0 

—84.0 

4556.3 

—33.7 

November 

4520.8 

-  69.2 

4652.9 

4-  62.9 

4550.0 

—40.0 

4575.2 

—14.8 

December 

4543.4 

-  46.6 

4643.5 

4-  53.5 

4568.3 

—21.7 

4584.9 

-  5.1 

1872  January 

4508.4 

-  81.6 

4621.0 

4-  31.0 

4537.9 

—52.1 

4556.0 

—34.0 

February 

4592.6 

4-     2.6 

4641.1 

+  51.1 

4615.3 

4-25.3 

4616.7 

4-26.7 

March 

4558.9 

-  31.1 

4644.7 

4-  54.7 

4585.4 

-  4.6 

4596.1 

4-  6.1 

April 

4567.8 

—  22.2 

4653.8 

4-  63.8 

4573.5 

—16.5 

4598.0 

4-  8.0 

May 

4561.6 

-  28.4 

4668.7 

4-  78.7 

4565.2 

—24.8 

4597.9 

4-  7.9 

June 

4578.1 

-  11.9 

4709.2 

4-119.2 

4564.8 

—25.2 

4617.7 

4-27.7 

July 

4567.8 

—  22.2 

4703.4 

4-113.4 

4567.5 

—22.5 

46  13.  4 

4-23.4 

August 

4548.4 

-  41.6 

4729.0 

4-139.0 

4544.1 

—45.9 

4606.6 

4-16.6 

September 

4538.8 

-  51.2 

4705.4 

4-115.4 

4556.6 

—33.4 

4599.8 

4-  9.8 

Mean  of  Year 

4547.4 

-  42.6 

4671.1 

4-  81.1 

4561.2 

—28.8 

4593.2 

4-  3.2 

BAROMETRIC  ALTITUDES. 


IX. 

COLFAX    AND    SUMMIT.     (THIRD  YEAE.) 


By  Railroad  Survey,  4590  feet. 


Date. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

1872  October 

4522.5 

-  67.5 

4701.9 

+111.9 

4566.2 

—23.8 

4597,6 

+  7.6 

November 

4488.9 

—101.1 

4648.8 

+  58.8 

4521.8 

—68.2 

4553.5 

—36.5 

December 

4494.1 

—  95.9 

4608.6 

+  18.6 

4518.5 

—71.5 

4539.5 

—50.5 

1873  January 

4531.1 

-  58.9 

4624.0 

+  34.0 

4555.8 

—34.2 

4569.9 

—20.1 

February 

4583.2 

—     6.8 

4667.2 

+  77.2 

4592.8 

+  2.8 

4613.5 

+23.5 

March 

4532.0 

-  58.0 

4658.9 

+  68.9 

4555.7 

—34.3 

4581.7 

—  8.3 

April 

4558.2 

-  31.8 

4662.5 

+  72.5 

4571.8 

—18.2 

4598.1 

+  8.1 

May 

4562.2 

-  27.8 

4724.8 

+134.8 

4572.2 

—17.8 

4619.6 

+29.6 

June 

4562.5 

-  27.5 

4710.8 

+120.8 

4582.7 

—  7.3 

4618.3 

+28.3 

July 

4573.7 

-  16.3 

4695.8 

+105.8 

4585.2 

-  4.8 

4618.2 

+28.2 

August 

4615.2 

-t-  25.2 

4744.1 

+154.1 

4643.2 

+53.2 

4667.7 

+77.7 

*  September 

4534.8 

—  55.2 

4701.3 

+111.3 

4534.3 

—55.7 

4590.5 

+  0.5 

Mean  of  Year 

4546.5 

-  43.5 

4679.1 

+  89.1 

4566.7 

—23.3 

4597.3 

+  7.3 

*  Mean  of  First  and  Second  Years. 


X. 


SACRAMENTO    AND    COLFAX.     (MEAN  OF  THREE  YEARS.) 


By  Railroad  Survey,  2399  feet. 


Month. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

October 

2357.3 

—41.7 

2452.6 

+53.6 

2357.3 

—41.7 

2388.4 

—10.6 

November 

2364.9 

—34.1 

2436.2 

+37.2 

2367.1 

—31.9 

2389.5 

—  9.5 

December 

2363.7 

—35.3 

2426.9 

+27.9 

2381.2 

—17.8 

2390.5 

—  8.5 

January 

2362.4 

—36.6 

2432.0 

+33.0 

2374.8 

—24.2 

2389.6 

-  9.4 

February 

2380.2 

—18.8 

2427.9 

+28.9 

2395.2 

—  3.8 

2401.0 

+  2.0 

March 

2393.3 

—  5.7 

2456.6 

+57.6 

2392.4 

-  6.6 

2414.2 

+15.2 

April 

2420.1 

+21.1 

2475.3 

+76.3 

2417.6 

+18.6 

2437.5 

+38.5 

May 

2432.9 

+33.9 

2478.8 

+79.8 

2410.0 

+11.0 

2440.4 

+41.4 

June 

2430.0 

+31.0 

2490.3 

+91.3 

2401.8 

+  2.8 

2440.5 

+41.5 

July 

2434.6 

+35.6 

2484.5 

+85.5 

2407.8 

+  8.8 

2442.4 

+43.4 

August 

2423.1 

+24.1 

2491.2 

+92.2 

2394.1 

-  4.9 

2436.5 

+37.5 

September 

2377.0 

—22.0 

2458.3 

+59.3 

2375.7 

—23.3 

2403.2 

+  4.2 

Mean 

2394.9 

-  4.1 

2459.2 

+60.2 

2389.6 

-  9.4 

2414.5 

+15.5 

80 


TABLES  OF 


XI. 


SACRAMENTO   AND    SUMMIT.     (MEAN  or  THEEE  YEAES.) 

By  Railroad  Survey.  6989  feet. 


Month. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

October 

6788.2 

—200.8 

7069.5 

+  80.5 

6829.6 

—159.4 

6896.2 

-  92.8 

November 

6798.6 

—190.4 

7029.5 

-4-  40.5 

6839.0 

—150.0 

6889.1 

-  99.9 

December 

6806.2 

—  182.8 

6976.5 

-  12.5 

6856.8 

—132.2 

6879.7 

—109.3 

January 

6823.4 

—165.6 

6980.5 

—     8.5 

6867.0 

—122.0 

6890.2 

—108.8 

February 

6924.2 

-  64.8 

7049.9 

+  60.9 

6962.8 

-  26.2 

6978.5 

—  20.5 

March 

6899.3 

-  89.7 

7065.9 

-4-  76.9 

6930.7 

-  58.3 

6965.1 

—  23.9 

April 

6965.2 

-  23.8 

7109.5 

-Hi  20.  5 

6955.9 

-  33.1 

7010.3 

+  21.3 

May 

6962.2 

-  26.8 

7126.8 

+137.8 

6932.0 

-  57.0 

7006.6 

+  17.6 

June 

6955.4 

-  33.6 

7136.6 

+147.6 

6921.2 

-  67.8 

7003.7 

+  14.7 

July 

6924.5 

-  64.5 

7106.5 

+117.5 

6915.7 

-  73.3 

6982.8 

6.2 

August 

6907.2 

-  81.8 

7137.7 

+148.7 

6906.7 

—  82.3 

6984.3 

4.7 

September 

6852.6 

—136.4 

7094.5 

+105.5 

6861.9 

—127.1 

6936.6 

-  52.4 

Mean 

6883.9 

—105.1 

7073.6 

+  84.6 

6898.3 

-  90.7 

6951.9 

-  37.1 

XII. 

COLFAX   AND   SUMMIT.     (MEAN  o?  THREI  YIABS.) 


Ry  Railroad  Survey,  4390  feet. 


Month. 

7A.M. 

2P.M. 

9P.M. 

Mean. 

October 

4493.2 

—96.8 

4671.0 

+  81.0 

4522.0 

—68.0 

4562.9 

—27.1 

November 

4493.7 

—96.3 

4638.7 

+  48.7 

4522.9 

—67.1 

4551.9 

—38.1 

December 

4497.1 

—92.9 

4612.0 

+  22.0 

4525.2 

—64.8 

4544.6 

—45.4 

January 

4507.7 

—82.3 

4617.1 

+  27.1 

4535.3 

—54.7 

4553.3 

—36.7 

February 

4564.4 

—25.6 

4648.8 

+  58.8 

4582.2 

-  7.8 

4598.2 

+  8.2 

March 

4544.0 

—  4C.O 

4651.3 

+  61.3 

4561.5 

—28.5 

4585.3 

-  4.7 

April 

4569.4 

—20.6 

4666.9 

+  76.9 

4559.5 

—30.5 

4598.6 

+  8.6 

May 

4573.7 

—16.3 

4694.6 

+104.6 

4557.7 

—32.3 

4608.6 

+18.6 

June 

4581.5 

-  8.5 

4713.1 

+123.1 

4567.7 

—22.3 

4620.9 

+30.9 

July 

4568.3 

—21.7 

4706.3 

+116.3 

4568.4 

—21.6 

4614.6 

+24.6 

August 

4568.1 

—21.9 

4733.9 

+143.9 

4571.2 

—18.8 

4624.2 

+34.2 

September 

4534.8 

—55.2 

4701.3 

+111.8 

4534.3 

—55.7 

4590.5 

+  0.5 

Mean 

4541.3 

—48.7 

4671.3 

+  81.3 

4550.7 

—39.3 

4587.8 

-  2.2 

EKRATUM. 

P,xge  80,  Table  XI..  4th  lino,  last  column,  under  <<  Mean,"  for  - 108.8, 
read  — 98.8. 


BAROMETRIC  ALTITUDES. 


81 


XIII. 

SACRAMENTO    AND    SUMMIT.     (FIRST  YEAR.) 


Date. 

187O 

Oct. 

VARIATION  FROM  RAILROAD  SURVEY. 

DIFFERENCES. 

Direct. 

With  intermediate  Station. 

7A.M. 

2P.  M. 

9P.  M. 

Mean 
of  Day. 

7  A.  M. 

2  P.  M. 

9  P.  II. 

Mean 
of  Day. 

7A.M. 

2  P.M. 

9  P.M. 

Mean 
of 
T>av. 

—210.6 

+  48.7 

—169.4 

—109.2 

—155.7 

-H  99.1 

—125.1 

—60.9 

54.9 

50.4 

44.3 

48.3 

Nov. 

—228.5 

+  17.9 

—171.5 

—  126.8 

—163.8 

-H   60.9 

—123.5 

—75.6 

64.7 

43.0 

48.0 

51.2 

Dec. 

—238.3 

—  25.5 

—171.1 

—144.5 

-177.3 

-H  30.2 

—  125.C 

—90.1 

61.0 

55.7 

45.5 

54.4 

1871 

Jan. 

—212.2 

-  27.9 

—165.6 

—135.1 

—152.3 

-H  42.6 

—114.2 

—74.7 

59.9 

70.5 

51.4 

60.4 

Feb. 

—137.3 

+  51.1 

-  68.4 

-  52.5 

-  99.5 

+  81.4 

-  45.1 

—21.9 

37.8 

30.3 

23.3 

30.6 

Mar. 

—101.6 

-f-  91.7 

-  73.6 

-  27.9 

—  59.6 

-HH6.5 

—  49.7 

+  2.0 

42.0 

24.8 

23.9 

29.9 

Apr. 

-  64.4 

-J-123.6 

-  94.6 

-  12.4 

—  20.9 

+155.2 

—  68.3 

+21.4 

43.5 

31.6 

26.3 

33.8 

May 

-  16.3 

-Hi  45.  3 

-  67.7 

+  19.8 

+  27.5 

+179.1 

-  41.8 

+  54.9 

43.8 

33.8 

25.9 

35.1 

June 

-  42.9 

-1-171.1 

-  97.6 

+     9.4 

-H  25.8 

+223.0 

-  46.7 

+68.0 

68.7 

52.8 

50.9 

58.6 

July 

—107.5 

-f-146.2 

—113.0 

—  23.9 

•     8.7 

+220.7 

-  37.3 

+58.8 

98.8 

74.5 

75.7 

82.7 

Aug. 

—149.5 

-Hi  65.  2 

—163.9 

-  48.8 

-  45.4 

+230.4 

—  83.2 

+34.3 

104.1 

65.2 

80.7 

83.1 

Sept. 

—132.1 

+126.1 

—152.4 

—  52.2 

-  80.3 

+187.8 

—105.1 

+  1.7 

51.8 

61.7 

47.3 

53.9 

Mean 

—136.8 

-H  86.1 

—125.7 

-  58.7 

-  75.9 

+135.7 

-  80.5 

-  6.8 

60.9 

49.5 

45.3 

51.8 

XIV. 

SACRAMENTO    AND    SUMMIT.     (SECOND  YEAR.) 


Date. 

VARIATION  FROM  RAILROAD  SURVEY. 

DIFFERENCES. 

Direct. 

With  intermediate  Station. 

7  A.  M. 

2  P.  M. 

9  P.  M. 

Mean 
of  Day. 

7  A.  M. 

2  P.  M. 

9  P.  M. 

Mean 
of  Day. 

7A.M. 

2P.M. 

9P.M. 

Mean 
of 
Day. 

1871 

Oct. 

—217.1 

+111.7 

—^78.3 

-  94.8 

—146.5 

+162.9 

—117.5 

-  33.8 

70.6 

51.2 

60.8 

61.0 

Nov. 

—163.2 

+  62.4 

—119.5 

—  73.8 

—107.7 

+103.2 

-  67.2 

—  23.9 

55.5 

40.8 

52.3 

49.9 

Dec. 

—120.2 

+     0.6 

-  76.3 

—  66.0 

-  66.5 

+  75.6 

-  15.8 

-     3.2 

53.7 

75.0 

60.5 

62.8 

1878 
Jan. 

—140.5 

-  24.4 

—  95.9 

-  86.8 

—108.8 

+  57.1 

-  62.2 

-  37.6 

31.7 

81.5 

33.7 

49.2 

Feb. 

-  29.8 

+  31.1 

-  10.7 

—     3.2 

-   13.0 

+  73.3 

+  14.2 

+  25.2 

16.8 

42.2 

24.9 

28.4 

Mar. 

-  59.8 

+  44.5 

-  37.5 

-  18.2 

—  28.1 

+  99.5 

—  12.6 

+  19.5 

31.7 

55.0 

24.9 

37.7 

Apr. 

—  20.9 

+  76.4 

—  28.0 

+     9.5 

+     5.3 

+118.6 

•     8.9 

+  38.2 

26.5 

42.2 

19.1 

28.7 

May 

-  52.7 

+  75.9 

-  84.9 

-  20.7 

+     5.0 

+143.4 

—  28.3 

+  40.0 

57.7 

67.5 

56.6 

60.7 

June 

-  38.1 

+  87.0 

—102.5 

-  18.1 

+  10.7 

+162.0 

-  37.5 

+  45.2 

48.8 

75.0 

65.0 

63.3 

July 

-  54.1 

+107.0 

—101.3 

-  15.9 

+  18.6 

+189.3 

-  20.6 

+  63.0 

72.7 

82.3 

80.7 

78.9 

Aug. 

—105.8 

+108.3 

—109.1 

-  35.8 

-  34.3 

+204.5 

-  70.7 

+  33.1 

71.5 

96.2 

38.4 

68.9 

Sept. 

—140.6 

+  84.9 

—101.7 

—  52.6 

-  73.3 

+154.6 

-  60.5 

+     5.7 

67.3 

69.7 

41.2 

58.3 

Moan 

—  95.2 

+  63.8 

-  87.1 

-  39.7 

-  44.9 

+128.7 

-  40.6 

+  14.3 

50.3 

64.9 

46.5 

54.0 

82 


TABLES  OF 


XV. 

SACRAMENTO    AND    SUMMIT.     (THIRD  YEAB.) 


Date. 

1873 
Oct. 

VARIATION  FROM  RAILROAD  SURVEY. 

DIFFERENCES. 

Direct. 

With  intermediate  Station. 

7  A.  M. 

2  P.  M. 

9P.M. 

Mean 
of  Day. 

7  A.  M. 

2  P.  M. 

9  P.  M. 

Mean 
of  Day. 

7A.M. 

2P.M. 

9P.1I. 

Mean 
of 
Dav. 

—174.8 

+  81.0 

—130.5 

-  74.3 

—113.7 

4-142.1 

—  83.0 

-  17.9 

61.1 

61.1 

47.5 

56.4 

Nov. 

—179.5 

-f-  41.3 

—159.1 

—  99.5 

—120.1 

4-  89.7 

—108.0 

-  46.1 

59.4 

48.4 

51.1 

53.1 

Dec. 
1873 

Jan. 

—189.9 
—144.1 

-  12.5 
+  26.7 

—149.3 
—104.5 

—117.5 
-  74.6 

—140.7 
-  95.6 

4-  43.9 
+  80.5 

—106.4 
-  60.5 

-  68.3 
-  25.8 

49.2 
48.5 

56.4 
53.8 

42.9 
44.0 

49.2 

48.8 

Feb. 

-  27.4 

+100.6 

4-     0.4 

4-  24.3 

-  20.7 

4-108.4 

—     3.9 

+  27.3 

6.7 

7.8 

-4.3 

3.0 

Mar. 

—107.6 

+  94.5 

-  63.8 

—  25.7 

-  67.3 

4-140.7 

-  42.8 

+  10.0 

40.3 

46.2 

21.0 

35.7 

Apr. 

+  13.8 

4-161.6 

4-  23.4 

+  66.7 

+  17.2 

4-185.6 

+  41.7 

+  81.9 

3.4 

24.0 

18.3 

15.2 

May 

-  11.3 

+192.3 

-  18.4 

4-  53.8 

+  20.5 

4-230.7 

+     6.0 

+  85.0 

31.8 

38.4 

24.4 

31.2 

June 

-  19.8 

4-184.8 

-     3.3 

4-  52.9 

4-  31.2 

4-257.  4 

+  25.7 

+104.0 

51.0 

72.6 

29.0 

51.1 

July 

-  31.8 

+  99.3 

-     5.7 

4-  21.3 

+  30.3 

4-189.1 

+  22.6 

+  80.4 

62.1 

89.8 

28.3 

59.1 

Aug. 

+  10.0 

4-172.7 

+  26.0 

4-  70.4 

+  85.5 

4-172.0 

+  84.3 

+148.2 

75.5 

-0.7 

58.3 

77.8 

Sept. 

—136.4 

4-105.5 

—127.1 

-  52.4 

-  71.7 

+174.7 

-  65.8 

+  12.2 

64.7 

69.2 

61.3 

64.6 

Mean 

-  83.2 

4-104.0 

-  59.3 

-  12.9 

-  37.1 

+159.9 

-  24.3 

+  32.7 

46.1 

55.9 

35.0 

45.6 

XVI. 

SACRAMENTO    AND   SUMMIT.      (MEAN  OF  THREE  YEARS.) 


VARIATION  FROM  RAILROAD  SURVEY. 

DIFFERENCES. 

Month. 

Direct. 

With  intermediate  Station. 

7A.M. 

2  P.  M. 

9  P.  M. 

Mean 
of  Day. 

7  A    M 

2  P.  M. 

9P.lt 

Mean 
of  Day. 

7A.M 

2PM. 

9P.M. 

Mean 
of 
Day. 

Oct. 

—200.8 

+  80.5 

—159.4 

—  92.8 

—138.5 

+134.6 

—109.7 

—37.7 

62.3 

54.1 

49.7 

55.1 

Nov. 

—190.4 

+  40.5 

—150.0 

--  99.9 

—130.4 

+  85.9 

-  99.0 

—47.6 

60.0 

45.4 

51.0 

52.3 

Dec. 

—182.8 

-  12.5 

—132.2 

-109.3 

—128.2 

+  49.9 

-  82.6 

—  53.9 

54.6 

62.4 

49.6 

55.4 

Jan. 

—165.6 

—    8.5 

—122.0 

—  98.8 

-118.9 

+  60.1 

-  78.9 

—46.1 

46.7 

68.6 

43.1 

52.7 

Feb. 

-  64.8 

+  60.9 

-  26.2 

-  10.5 

-  44.4 

+  87.7 

-  11.6 

+10.2 

20.4 

26.8 

14.6 

20.7 

Mar. 

-  89.7 

+  76.9 

-  58.3 

-  23.9 

-  51.7 

+118.9 

-  35.1 

+10.5 

38.0 

42.0 

23.1 

34.4 

Apr. 

-  23.8 

+120.5 

-  33.1 

+  21.3 

+     0.5 

+153.2 

-  11.9 

+47.1 

24.3 

32.7 

21.2 

25.8 

May 

-  26.8 

+137.8 

-  57.0 

+  17.6 

+  17.6 

+184.4 

-  21.3 

+60.0 

44.4 

46.6 

35.7 

42.4 

June 

-  33.6 

+147.6 

-  67.8 

+  14.7 

+  22.5 

+214.4 

-  19.5 

+72.4 

56.1 

66.8 

48.3 

57.7 

July 

-  64.5 

+117.5 

—  73.3 

-    6.2 

+  13.9 

+201.8 

-  12.8 

+68.0 

78.4 

84.3 

60.5 

74.2 

Aug. 

-  81.8 

+148.7 

-  82.3 

4.7 

+     2.2 

+236.1 

-  23.7 

+71.7 

84.0 

87.4 

58.6 

76.4 

Sept. 

—136.4 

+105.5 

—127.1 

-  52.4 

-  77.2 

+170.6 

-  79.0 

+  4.7 

59.2 

65.1 

48.1 

57.1 

Mean 

—105.1 

+  84.6 

-  90.7 

-  37.1 

-  52.7 

+141.5 

—  48.7 

+13.3 

52.4 

56.9 

42.0 

50.4 

BAROMETRIC   ALTITUDES. 


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BAROMETRIC   ALTITUDES. 


85 


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86 


TABLES   OF 


XX. 


APPROXIMATE  ERROR  OF  BAROMETRIC  MEASUREMENTS 
BETWEEN  SACRAMENTO  AND   COLFAX. 

By  Railroad  Survey,  2jgg  feet. 


Hour. 

Jan. 

Feb. 

Mar. 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean 
of 
Year. 

7A.M. 

-32 

-19 

-   4 

+17 

+30 

+27 

+24 

+  7 

-26 

-43 

-37 

-35 

-  8 

2P.M. 

+27 

+30 

+56 

+67 

+77 

+86 

+85 

+80 

+58 

+54 

+38 

+29 

+57 

9P.M. 

-19 

-  7 

-  4 

+19 

+13 

+10 

+  3 

-13 

-29 

-38 

-31 

-23 

-10 

Mean 
of  Day. 

-  8 

0 

+16 

+33 

+39 

+40 

+37 

+24 

0 

-  9 

-10 

-  8 

+13 

XXI. 


APPROXIMATE  ERROR  OF  BAROMETRIC  MEASUREMENTS 
BETWEEN  SACRAMENTO   AND   SUMMIT. 

By  Railroad  Survey,  (K)8<)  feet. 


Hour. 

Jan. 

Feb. 

Mar. 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean 
of 
Year. 

7A.M. 

-165 

-100 

-76 

-    26 

-   28 

-  36 

-   70 

-  90 

-136 

-200 

-200, 

-190 

-110 

2P.M. 

-  10 

+    54 

+78 

+  106 

+130 

+146 

+132 

+126 

+104 

+  80 

+  40 

-  12 

+  81 

9P.M. 

-125 

-  58 

-52 

-  32 

-  42 

-  70 

-  82 

-  90 

-124 

-1G2 

-156 

-142 

-  94 

Mean 
of  Day. 

-100 

-  35 

-17 

+  16 

+  20 

+  13 

7 

-  18 

-  52 

-  94 

-105 

-115 

-  41 

XXII. 


APPROXIMATE  ERROR  OF  BAROMETRIC  MEASUREMENTS 
BETWEEN  COLFAX  AND  SUMMIT. 

By  Railroad  Survey,  4-90  feet. 


Hour. 

Jan. 

Feb. 

Mar. 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean 
of 
Year. 

7A.M. 

-84 

-45 

-40 

-24 

-  16 

-  14 

-   22 

-  30 

-  56 

-98 

-96 

-93 

-51 

2P.M. 

+28 

+54 

+62 

+75 

+100 

+124 

+122 

+120 

+112 

+84 

+50 

+24 

+80 

9P.M. 

-58 

-32 

-30 

-26 

-  24 

-  20 

-  22 

-  30 

-56 

-70 

-68 

-6G 

-42 

Mean 
of  Day. 

-38 

-  8 

-  3 

+  8 

+  20 

+  30 

+  26 

+  12 

0 

-28 

-38 

-45 

-  5 

BAROMETRIC  ALTITUDES. 


87 


XXIII. 


CORRECTIONS  TO  BE  APPLIED  FOR  EACH  THOUSAND  FEET  FROM 
SEA-LEVEL  TO   2400  FEET. 


Hour. 

Jan. 

Feb. 

Mar. 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean 
of 
Year. 

+  3.3 

7A.M 

+13.3 

+  7.9 

+  1.7 

-  7.1 

-12.5 

-11.2 

-10.0 

-  2.9 

+10.8 

+  17.9 

+  15.4 

+14.6 

8    " 

+    8.2 

+    2.5 

-    4.0 

-  12.3 

-17.4 

-  16.6 

-  15.0 

-    9.1 

+    3.1 

+    9.6 

+  11.6 

+  10.7 

-    l.C 

9    " 

+    2.8 

-3.4 

-    9.7 

-16.7 

-  21.5 

-21.5 

-  19.7 

-14.4 

-    3.6 

+    1.0 

+    6.9 

+    5.7 

-    6.1 

10    " 

-    3.5 

-    7.0 

-  14.2 

-20.5 

-  25.0 

-  25.7 

-23.7 

-  19.0 

-    9.5 

-    6.4 

+    0.5 

-    0.4 

-  10.4 

11    " 

-    6.8 

-    9.6 

-17.5 

-23.4 

-27.8 

-  29.0 

-  27.4 

-  23.0 

-15.0 

-  12.0 

-    6.4 

-    5.0 

-14.5 

12  M. 

-    9.2 

-  11.0 

-20.0 

-  25.6 

-29.6 

-31.8 

-  30.4 

-26.5 

-19.6 

-17.0 

-  12.3 

-    8.5 

-  18.6 

1  P.M. 

-10.5 

-  12.0 

-21.9 

-  27.2 

-31.0 

-  34.0 

-  33.3 

-  30.2 

-22.7 

-21.0 

-15.3 

-  11.0 

-21.7 

2    " 

-11.2 

-12.5 

-23.3 

-27.9 

-32.1 

-35.8 

-35.4 

-33.3 

-24.2 

-22.5 

-15.8 

-12.1 

-23.7 

3   " 

-10.0 

-12.0 

-21.4 

-  27.9 

-32.0 

-  36.5 

-  36.0 

-34.1 

-23.2 

-20.7 

-15.0 

-10.5 

-21.0 

4    " 

-    7.8 

-    9.6 

-17.9 

-24.8 

-30.4 

-36.0 

-33.9 

-32.2 

-19.7 

-16.0 

-11.2 

-    7.8 

-  16.9 

5    " 

-    4.0 

-    6.6 

-12.5 

-20.4 

-27.1 

-31.1 

-29.4 

-  26.3 

-15.0 

-    8.7 

-    4.8 

-    4.0 

-11.9 

6    " 

0 

-    2.8 

-    6.0 

-16.0 

-21.5 

-23.3 

-  20.4 

-16.2 

-    6.0 

0 

+    3.5 

+    0.7 

-    6.4 

7   " 

+    2.1 

+    1.0 

-    2.2 

-  12.5 

-  14.4 

-13.0 

-  11.0 

-    4.3 

+    4.5 

+    7.8 

+    8.9 

+    6.3 

-    1.6 

8   " 

+    5.2 

+    2.8 

+    0.4 

-    9.3 

-    8.0 

-    6.4 

-    5.0 

+    3.3 

+    9.5 

+  12.6 

+  11.5 

+    8.2 

+    2.0 

9   " 

+  7.9 

+  2.9 

+  1.7 

-  7.9 

-  5.4 

-  4.2 

-  1.2 

+  5.4 

+  12.1 

+  15.8 

+  12.9 

+  9.6 

+  4.1 

Mean 
of 
Day. 

+  3.3 

0 

-  6.6 

-13.7 

-16.2 

-16.7 

-15.4 

-10.0 

0 

+  3.7 

+  4.2 

+  3.3 

-  5.4 

XXIV. 


CORRECTIONS  TO   BE  APPLIED  FOR  EACH  THOUSAND  FEET  FROM 
SEA-LEVEL  TO  7000  FEET. 


Hour. 

Jan. 

Feb. 

Mar. 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean 
of 
Year. 

?A.M. 

+23.6 

+  14.3 

+10.9 

+  3.7 

+  4.0 

+  5.1 

+10.0 

+12.9 

+  19.4 

+28.6 

+28.6 

+  27.1 

+  15.7 

8    " 

+  21.9 

+  12.4 

+    8.7+    1.0 

+    1.5 

+    1.4 

+    6.6+    8.7 

+  16.2 

+  24.8 

+  26.4 

+  25.4 

+  13.3 

9    " 

+  19.2 

+    9.6+    5.5 

-    1.8 

-    1.8 

-    2.7 

+    2.3+    4.4 

+  11.1 

+  19.6 

+  22.1 

+  22.5 

+    9.4 

10    " 

+  16.0 

+    6.6 

+    2.6 

-    4.6 

-    5.0 

-    6.8 

-    2.4-    0.4 

+    4.8 

+  12.8 

+  16.9 

+  19.0 

+    5.3 

11    " 

+  11.2 

+    2.6 

-    1.0 

-    7.5 

-    8.7 

-10.7 

-    7.3-    5.5-    1.5 

+    5.8 

+    9.0 

+  13.8 

0 

12  M. 

+    6.6 

-    1.6 

-    4.7 

-10.8 

-13.3 

-15.5 

-12.9 

-11.3-    8.0 

-    1.0 

+    1.9 

+    8.0 

-    5.0 

1  P.M 

+    3.3 

-    6.0 

-    9.0 

-  14.0 

-17.0 

-  19.0 

-17.0 

-  16.0 

-12.7 

-    6.8 

-    2.8 

+    4.0 

-    9.0 

2    " 

+  1.4 

-    7.7 

-11.3 

-15.1 

-18.6 

-20.9 

-18.9 

-18.0 

-14.9 

-11.4 

-  5.7 

+  1.7 

-11.6 

3    " 

+    3.2 

-    6.3 

-    9.5 

-13.0 

-18.2 

-  21.6 

-19.1 

-18.4 

-  15.2 

-    9.2 

-    2.8 

+    3.8 

-    9.8 

4    " 

+    7.3 

-3.4 

-    6.7 

-    9.6-14.3 

-  20.0 

-16.2-15.0 

-11.1 

-    5.4 

+    1.8 

+    8.6 

-    5.7 

5    " 

+  11.1 

+    0.2-    3.1 

-    5.8-    8.8 

-15.4 

-10.7-    9.1 

-    4.0 

+    0.4 

+    7.0 

+  12.6 

-    0.4 

6    " 

+  14.4 

+    3.0+    0.4 

-    2.2-    3.4 

-    9.7 

-    4.5-    2.5 

+    5.0 

+    8.3 

+  12.2 

+  15.5 

+    5.1 

7    " 

+  16.3 

+    5.4+    3.5+    0.8:+    1.2 

-    2.0 

+    1.8+    4.0 

+  12.5 

+  16.5 

+  17.5 

+  18.0 

+    9.1 

8    " 

+  17.2 

+    7.3+    6.0 

+    3.5+    4.6 

+    5.3 

+    8.0+    9.6 

+  16.5 

+  21.6 

+  21.3 

+  19.5 

+  12.2 

9   " 

+  17.9 

+  8.3 

+  7.4  +  4.6  +  6.0 

+10.0 

+  11.7+12.9 

+  17.7 

+  23.1 

+22.3 

+20.3 

+13.4 

Mean 
of 
Day 

+  14.3 

+  5.0 

+  2.4 

-  2.3 

-  2.9 

-  1.9 

+  1.0 

+  2.6 

+  7.4 

+13.4 

+  15.0 

+  16.4 

+  5.9 

88 


TABLES  OF  BAROMETRIC  ALTITUDES. 


XXV. 


CORRECTIONS    TO    BE    APPLIED    FOR    EACH    THOUSAND  FEET   OF 

DIFFERENCE  OF  LEVEL  BETWEEN  THE  ALTITUDES 

OF    2400    AND    7000    FEET. 


Hour. 

Jan. 

Feb. 

Mar. 

+  8.7 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Mean 
of 
Year. 

7A.M. 

+18.3 

+  9.8 

+  5.2 

+  3.5 

+  3.0 

+  4.8 

+  6.5 

+12.2 

+  21.3 

+20.9 

+20.2 

+  11.1 

8   " 

+  16.4 

+    7.6 

+    5.5 

+    2.5 

+    0.7 

-    1.0 

+    1.0 

+    3.0 

+    8.7 

+  17.0 

+  17.8 

+  18.0 

+    8.0 

9   " 

+  13.7 

+    4.9 

+    2.3 

-    0.6 

-    3.0 

-    5.0 

-    2.8 

-    1.0 

+    4.4 

+  11.0 

+  14.6 

+  15.5 

+    3.8 

10   " 

+  10.3 

+    1.7 

-    1.2 

-    3.9 

-    7.0 

-    9.6 

-    7.3 

-    5.5 

-    0.3 

+    3.6 

+    9.8 

+  12.1 

-    0.5 

11    " 

+    6.2 

-    2.3 

-    5.3 

-    7.6 

-11.0 

-14.5 

-12.6 

-10.3 

-    6.1 

-    4.0 

+    4.0 

+    7.8 

-    5.4 

12  M. 

+    0.4 

-    7.3 

-  10.0 

-  11.5 

-15.7 

-20.7 

-19.4 

-17.0 

-14.5 

-11.0 

-    3.5 

+    1.5 

-11.6 

1    P.M. 

-    4.7 

-10.9 

-12.1 

-15.1 

-20.4 

-25.5 

-24.7 

-  24.0 

-22.2 

-16.7 

-  10.2 

-    3.9 

-16.1 

2    " 

-  6.1 

-11.7 

-13.5 

-16.3 

-21.7 

-27.0 

-26.5 

-26.1 

-24.3 

-18.3 

-10.9 

-  5.2 

-17.4 

3    " 

-    3.5 

-    9.3 

-11.4 

-14.0 

-21.0 

-27.4 

-26.3 

-  25.0 

-22.1 

-  15.0 

-    7.0 

-    2.0 

-15.0 

4    " 

+    0.6 

-    5.4 

-    7.8 

-10.7 

-17.3 

-23.5 

-22.0 

-  19.4 

-16.3 

-    9.4 

-    1.7 

+    2.0 

-10.7 

5   " 

+    5.2 

-    1.0 

-    3.7 

-    7.0 

-12.4 

-16.8 

-  15.0 

-13.3 

-    9.6 

-    2.5 

+    4.0 

+    6.4 

-    6.0 

6   " 

+    9.4 

+    2.8 

-    0.7 

-    3.4 

-    7.0 

-  10.4 

-    8.5 

-    7.1 

-    2.0+    4.5 

+    8.0 

+  10.3 

-    0.9 

7   " 

+  11.7 

+    5.7 

+    2.4 

0 

-    2.0 

-    4.3 

-    3.0 

-    2.0 

+    5.0 

+  10.2 

f  11.6 

+  12.5 

+    3.7 

8   " 

+  12.5 

+    6.8 

+    5.0 

+    3.3 

+    2.6 

+    0.8 

+    1.8 

+    3.4 

+  10.2 

+  14.5 

+  13.4 

+  13.8 

+    7.3 

9   " 

+12.6 

+  7.0 

+  6.5 

+   5.7 

+  5.2 

+  4.3 

+  4.8 

+  6.5 

+  12.2 

+15.2 

+  14.8 

+14.3 

+  9.1 

Mean 
of 
Day. 

+  8.3 

+  1.7 

+  0.7 

-  1.7 

-  4.3 

-  6.5 

-  5.7 

-  4.3 

0 

+  6.1 

+  8.3 

+  9.8 

+   1.1 

SUPPLEMENTARY  CHAPTER. 

(OCTOBER,  1878.) 

SINCE  the  publication  of  the  three  preceding  chapters,  with  the  accom- 
panying tables,  the  task  of  computing  the  altitudes  of  several  hundred 
points,  at  which  barometric  observations  were  taken  by  the  different  field 
parties  of  the  California  survey  during  the  seasons  of  1870  and  1871,  has 
been  completed.  The  work  has  been  pushed  to  a  conclusion  as  rapidly  as 
circumstances  would  allow,  but  progress  has  been  of  necessity  slow,  for  a 
great  part  of  the  labor  has  had  to  be  performed  at  such  times  only  as  could 
be  spared  from  regular  college  duties. 

The  present  chapter  is  intended  to  illustrate  more  fully  than  has  here- 
tofore been  possible  the  practical  value  of  the  special  tables  of  corrections 
prepared  for  use  in  California,  and  to  show  to  what  extent  their  use  will  be 
of  advantage  in  securing  a  closer  approximation  to  the  truth  than  can  be 
hoped  for  without  them ;  especially  in  cases  where  only  single  observations 
or,  at  best,  short  series  of  observations  are  available.  The  examples  chosen 
for  purposes  of  illustration  have  all  been  taken  from  the  work  of  the  years 
1870  and  1871,  for  the  reason  that  during  those  years  barometric  observa- 
tions were  taken  more  systematically  and  thoroughly  than  they  have  been 
either  before  or  since  in  the  history  of  the  survey,  and  the  observations  have 
been  reduced  with  particular  reference  to  the  problem  at  present  under 
discussion. 

There  were  three  active  field  parties  engaged  on  the  work  of  the  survey 
in  1870  :  one  was  in  the  field  from  the  first  of  May  to  the  first  of  August, 
occupied  for  the  most  part  in  Owen's  Valley,  and  the  mountainous  region 
of  Inyo  and  Mono  counties;  a  second  spent  the  months  of  September, 
October,  and  November  in  the  neighborhood  of  Clear  Lake,  in  the  Coast 
Ranges,  north  of  the  Bay  of  San  Francisco ;  and  a  third  was  employed  from 


90  BAROMETRIC  HYPSOMETRY. 

early  in  the  season  until  the  month  of  December  in  the  auriferous  gravel 
districts  of  Yuba,  Nevada,  and  Placer  counties.  The  organization  of  the  first 
two  parties  was  essentially  the  same,  Messrs.  Hoffmann  and  Craven  being 
in  charge  of  the  topographical  part  of  the  work,  and  Mr.  Goodyear  of  the 
geological ;  Mr.  Eabe  was  an  efficient  aid  in  the  barometric  work.  The  field- 
work  in  the  gravel  district  was  begun  in  May  by  Mr.  Bowman,  who  was 
joined  early  in  July  by  Mr.  Pettee.  Several  other  persons,  not  otherwise 
connected  with  the  survey,  gave  valuable  assistance  in  the  barometric  work 
from  time  to  time  at  places  where  it  was  found  convenient  to  establish 
stations  of  reference  as  the  work  progressed.  The  field-work  of  1871  was 
confined  almost  exclusively  to  Mr.  Goodyear's  examination  of  the  gravel  dis- 
tricts of  Placer,  El  Dorado,  and  Amador  counties.  The  barometers  in  use 
were  all  mercurial  cistern  barometers,  made  by  James  Green  of  New  York. 

The  number  of  different  points  at  which  observations  for  the  determina- 
tion of  altitude  were  taken  was  a  little  more  than  seven  hundred,  but  the 
total  number  of  separate  computations,  which  have  been  made  in  the  course 
of  the  work,  amounts  to  over  two  thousand.  Each  computation  has  been 
made  by  itself  without  regard  to  others,  for  the  sake  of  bringing  into  promi- 
nence, as  far  as  possible,  the  effects  of  times  and  seasons  upon  the  final 
results.  The  method  employed  was  as  follows.  The  barometric  data  for 
each  computation  were  first  freed  from  instrumental  errors  and  reduced  to  a 
common  standard.  Then  followed  the  computation  according  to  William- 
son's tables,  no  account  being  taken  of  the  moisture  in  the  atmosphere.  The 
corrections  for  temperature,  for  latitude,  and  for  the  decrease  of  gravity  were 
all  made  in  the  usual  order.  This  led  to  what  has  been  regarded  heretofore 
as  the  final  and  best  result  obtainable  from  the  data  employed.  In  what 
follows  in  this  chapter  this  result  will  be  called  the  uncorrected  result,  or  the 
uncorrected  difference  of  altitude.  The  next  step  was  to  apply  an  additional 
correction  derived  from  the  new  tables.  In  deciding  upon  the  proper  value 
to  be  assigned  to  this  correction  in  particular  cases  there  was  occasionally 
some  ground  for  doubt  and  a  difference  of  opinion,  the  tables  not  being  suf- 
ficiently extensive  to  meet  all  requirements.  Having  been  prepared  from 
observations  taken  at  only  three  stations,  Sacramento,  Colfax,  and  Summit, 
they  cannot  be  expected  to  furnish  precise  corrections  for  other  places.  For 
instance,  when  one  of  the  two  stations  involved  in  a  computation  was  Sacra- 
mento, and  the  other  was  a  point  midway  in  altitude  between  Colfax  and 


SUPPLEMENTARY  CHAPTER.  91 

Summit,  the  question  would  arise  whether  the  Sacramento-Colfax  (XXIII.), 
or  the  Sacramento-Summit  (XXIV.)  table  was  to  be  preferred.  In  other 
cases  doubts  would  arise  from  the  fact  that  both  the  field  station,  and  the 
corresponding  station  which  was  in  all  other  respects  the  best  for  reference, 
were  considerably  different  in  altitude  from  either  Sacramento,  Colfax,  or 
Summit.  Furthermore,  the  tables,  being  based  upon  monthly  averages,  must 
be  looked  upon  as  strictly  applicable  to  the  middle  portions  of  each  month 
only.  These  difficulties  were  overcome,  sometimes  in  one  way  and  some- 
times in  another,  but  always  with  a  view  of  getting  that  value  for  the  cor- 
rection which  was  the  most  probable,  after  taking  into  account  all  the 
circumstances  and  conditions  which  could  affect  it.  Fortunately,  the  amount 
of  error  in  the  final  results,  dependent  upon  any  uncertainty  which  might 
attach  to  the  determination  of  the  value  of  this  correction,  is  in  no  case  of 
material  importance.  The  quantities  involved  are  neither  absolutely  nor 
relatively  large.  In  all  the  numerical  work  every  precaution  was  taken 
to  secure  accuracy,  and  it  is  hoped  that  no  important,  error  has  escaped 
correction. 

For  each  one  of  about  four  hundred  points,  out  of  the  seven  hundred 
visited,  only  a  single  computation  for  altitude  has  been  made,  either  for  the 
reason  that  only  one  observation  was  taken  at  the  field  station,  or  because 
the  several  observations  taken  were  so  related  to  each  other,  and  to  the 
records  at  the  corresponding  stations,  that  only  one  really  independent 
computation  was  practicable.  The  cases  of  this  class  are,  of  course,  of  no 
value  in  illustrating  the  use  of  the  new  tables. 

In  one  hundred  and  forty-six  cases  computations  have  been  made  to  show 
the  differences  of  altitude  between  the  field  station  and  two  or  more  corre- 
sponding station^,  the  altitudes  of  which  have  been  determined  by  accurate 
spirit-level  survWs,  or  from  barometric  observations  extending,  with  a  few 
exceptions,  over  considerable  intervals  of  time.  If  the  tables  in  ordinary  use 
gave  accurate  results,  it  Is  evident  that  the  calculated  altitudes  above  the 
level  of  the  sea  of  any  one  of  these  one  hundred  and  forty-six  stations  ought 
to  be  the  same,  whatever  point  might  be  chosen  as  corresponding  station  or 
station  of  reference.  For  example,  the  calculated  altitude  of  Lowell  Hill 
ought  to  be  the  same,  whether  the  corresponding  station  barometer  was  ob- 
served at  Colfax  or  at  Summit.  As  a  matter  of  fact,  in  this  particular  ex- 
ample the  uncorrected  results,  obtained  in  the  usual  way,  differed  from  each 


92 


BAROMETRIC  HYPSOMETRY. 


other  by  118.6  feet.  The  corrected  results  differed  by  only  29.2  feet.  This 
comparatively  close  agreement  of  the  results  obtained  by  the  use  of  the  new 
tables  is,  as  far  as  it  goes,  a  good  piece  of  evidence  in  their  favor,  and  shows 
that  either  one  of  the  corrected  results,  taken  by  itself,  is  probably  consider- 
ably nearer  the  truth  than  either  of  the  uncorrected  ones.  It  would  extend 
this  chapter  to  an  unreasonable  length  to  give  the  details  of  all  the  cases 
which  bear  upon  this  phase  of  the  subject.  For  the  purposes  of  illustration 
the  cases  cited  in  the  following  table  have  been  chosen.  The  column  in  the 
table  headed  "  Uncorrected  Results  "  contains  the  computed  altitudes  of  the 
field  stations  above  the  sea,  determined  independently  of  each  other,  and 
without  the  use  of  the  new  tables.  The  column  of  "  Corrected  Results  "  gives 
the  final  determinations  of  altitude  after  the  application  of  the  corrections. 
The  columns  of  "  Differences  "  show,  at  a  glance,  how  great  the  disagreement 
is  in  each  case. 

ALTITUDES    COMPUTED  WITH    REFERENCE    TO    DIFFERENT    CORRESPONDING 

STATIONS. 


Field  Station. 

Corresponding 
Stations. 

Uncorrected 
Results. 

Difference. 

Corrected 
Results. 

Difference. 

1 

2 
3 

McKune's. 

Summit  of  road  on  Pet 
Hill. 

"Lava  Castle." 

Smartsville  .  .  . 
Nevada  City.. 

Smartsville  .  .  . 
Nevada  City.  . 

Colfax  

3006.0 
2930.3 

1641.6 
1621.2 

6621  0 

75.7 
20.4 

2941.0 

2930.3 

1624.4 
1637.9 

6530.6 

10.7 
13.5 

4 

Lava  Summit  near  Lib- 

Summit   
Colfax  

6485.2 
4472.7 

135.8 

6516.9 
4463.9 

13.7 

5 

erty  Hill. 
Reed's. 

Summit  
Colfax  

4447.3 
393.6 

25.4 

4458.4 
418.0 

5.4 

6 

7 

Camp  60  (Inyo  trip). 
Camp  11  (Kelsey  Creek). 

Sacramento  .  .  . 

Dutch  Flat  ... 
Summit  

Colfax  

453.8 

5151.4 
5187.5 

1398  2 

60.2 
36.1 

448.7 

5164.4 
5183.9 

1392  7 

30.7 
19.5 

Sacramento... 

1371.3 

26.9 

1375.2 

17.5 

SUPPLEMENTARY  CHAPTER. 


93 


Field  Station. 

Corresponding 
Stations. 

Uncorrected 
Results. 

Difference. 

Corrected 
Results. 

Difference. 

8 

Colfax  

1402  1 

1388  9 

q 

Secret  House. 

Sacramento... 
Colfax  

1333.6 
5503  6 

68.5 

1350.4 
5440  0 

38.5 

Summit  

5371  1 

132.5 

5405  3 

34.7 

10 

Crest  of  ridge   back   of 

Colfax  

4908  4 

48680 

Startown. 

Summit  

48140 

94.4 

4873.8 

5.8 

11 

Ford's  Bar. 

Colfax  

796.8 

845.0 

12 

Big  Trees,    above    Last 

Sacramento  .  .  . 
Colfax  

912.5 

5287.8 

115.7 

886.4 
5215.7 

41.4 

Chance. 

Summit.  . 

5151  3 

136.5 

5198  3 

17.4 

13 

Wilcox's  Meadows. 

Georgetown  .  .  . 
Summit  

5398.7 
5313  9 

84.8 

5332.1 
5355.2 

23.1 

14 

Marble  Valley. 

Colfax  

889.2 

911.7 

16 

Mule  Canon. 

Sacramento  .  .  . 
Colfax  

952.5 
2832.2 

63.3 

939.0 
2833.0 

27.3 

16 

Klipstein's. 

Morison's  
Colfax  

2815.4 
4138.9 

16.8 

2804.0 
4173.8 

29.0 

Summit  ....    . 

4119.8 

19.1 

4060.6 

113.2 

17 
18 

Bridge  near  Leavitt's. 
Point  on  Cosumnes  River. 

Nevada  City.  . 
Dutch  Flat  ... 

Colfax  

5717.0 
5720.7 

1685.0 

3.7 

5632.5 
5654.4 

1699.1 

21.9 

Sacramento  .  .  . 

1675.3 

9.7 

1643.8 

55.3 

With  one  exception  the  results  given  in  this  table  are  based  upon  one  or 
at  most  two  observations  only.  The  exception  is  No.  7,  that  of  Camp  11  on 
Kelsey  Creek,  for  which  point  the  altitudes  given  are  the  means  derived  from 
forty  independent  computations  for  both  Sacramento  and  Colfax.  The  ob- 
servations used  in  the  computations  were  those  taken  at  9  p.  M.,  October  1st, 
and  at  7  A.  M ,  2  P.  M.,  and  9  p.  M.  from  the  2d  to  the  12th  inclusive,  and  on 


94  BAROMETRIC   HYPSOMETRY. 

the  16th  and  17th.  That  is  to  say,  they  represent  very  nearly  the  daily 
means  for  the  first  half  of  the  mouth  of  October.  With  a  series  of  observa- 
tions so  extensive  as  this,  it  would  seem  as  if  a  still  closer  accordance  might 
be  expected,  but  there  were  among  the  eighty  results  a  few  of  an  abnormal 
character  for  which  no  explanation  can  be  given.  They  may  have  been  due 
to  a  lack  of  care  on  the  part  of  the  observers,  but  they  are  not  so  obviously 
erroneous  as  to  justify  their  rejection. 

An  inspection  of  the  columns  of  differences  shows  very  plainly  that,  in 
the  first  fourteen  cases  cited,  the  use  of  the  new  tables  has  brought  widely 
discordant  results  into  a  considerably  closer  agreement.  Absolute  identity 
in  computations  of  this  kind  will  not  be  looked  for  by  any  one  familiar  with 
the  subject.  Even  under  the  most  favorable  circumstances  there  are  liable 
to  be  local  peculiarities,  at  one  or  at  both  of  the  stations,  which  will  have  an 
influence  upon  the  barometer  or  thermometer,  for  which  no  allowance  can  be 
made ;  or  small  undetected  errors  in  the  reading  of  the  scales  on  the  instru^ 
ments  will  be  magnified  in  the  numerical  work  which  follows  ;  and  unless  a 
record  is  kept  of  all  the  more  important  meteorological  phenomena,  especially 
of  the  direction  and  force  of  the  wind,  and  of  the  presence  or  absence  of 
clouds,  in  connection  with  the  ordinary  observations  for  barometric  pressure 
and  for  temperature,  thp  computer  will  be  in  no  position  to  judge  whether 
the  corrections,  particularly  that  for  temperature,  which  is  almost  always 
much  the  largest  of  them  all,  are  overestimated  or  underestimated. 

Not  unfrequently,  indeed,  the  atmospheric  or  local  conditions  are  decid- 
edly unfavorable  for  the  accurate  determination  of  altitudes  with  the  barom- 
eter. If  the  day  is  warm,  and  the  sky  is  bright  and  clear  at  one  station,, 
while  at  the  other  a  gathering  thunder-storm  causes  a  rapid  cooling  of  the 
atmosphere,  it  is  evident  that  the  readings  of  the  thermometers  at  the  two 
stations  do  not  furnish  sufficient  data  to  enable  one  to  form  any  just  esti- 
mate of  the  mean  temperature  of  the  intervening  air  column.  It  will  not  be 
a  matter  of  surprise,  therefore,  that  the  uncorrected  results  sometimes  agree 
with  each  other  even  more  closely  than  the  corrected  ones  do.  The  cases 
numbered  from  15  to  18  in  the  table  are  of  this  character.  Of  course  no 
provision  can  be  made  in  tables  of  corrections  for  such  emergencies,  and  if  it 
had  been  found,  as  the  result  of  the  examination  of  a  large  number  of  cases, 
that  the  use  of  such  tables  led  as  often  or  to  as  great  an  extent  to  the  in- 
crease of  discrepancies  as  it  did  to  their  removal,  there  would  certainly  be 


SUPPLEMENTARY  CHAPTER.  95 

little  to  hope  for  in  carrying  the  investigation  further  in  this  direction.  In 
thirty-six  of  the  one  hundred  and  forty-six  cases  now  under  consideration, 
or  nearly  twenty-five  per  cent,  the  use  of  the  new  tables  of  corrections  in- 
creases to  a  greater  or  less  extent  (in  one  or  two  instances  quite  largely)  the 
discrepancies  in  the  computed  results.  This  number  is  so  large  that  it  would 
afford  a  reasonable  basis  for  doubt  as  to  the  general  trustworthiness  of  the 
tables,  unless  it  could  be  shown  that  there  was  something  abnormal  or  out 
of  the  usual  course  in  the  original  observations  or  in  the  accompanying 
circumstances. 

In  five  of  these  thirty-six  imfavorable  cases  the  field  stations  were  in 
Mono  County,  while  the  corresponding  stations  were  at  Nevada  City  and 
Dutch  Flat,  —  points  hardly  twelve  miles  apart,  but  about  a  hundred  miles 
distant  from  the  field  stations,  and  on  the  opposite  slope  of  the  Sierra  Nevada 
Mountains.  (See  No.  17  in  the  table.)  The  tables  of  corrections  are  surely 
not  chargeable  with  failure  under  conditions  so  radically  different  from  those 
for  which  they  were  calculated.  In  five  other  cases,  one  of  which  is  No.  16 
in  the  table,  the  field  observations  were  taken  on  the  25th  and  26th  of 
November,  just  at  the  beginning  of  what  proved  to  be  a  long  and  severe 
snow-storm.  Probably  the  atmospheric  disturbance  was  already  so  far  ad- 
vanced as  to  affect  materially  any  computations  based  upon  a  formula  which 
presupposes  a  condition  of  atmospheric  equilibrium.  In  four  cases,  one  of 
which  is  No.  15  in  the  table,  either  the  field  station  or  one  of  the  corre- 
sponding stations  was  near  the  border  of  Clear  Lake,  a  sheet  of  water  having 
an  area,  approximately,  of  a  hundred  square  miles.  It  is  not  unreasonable 
to  suppose  that  this  large  body  of  water,  nearly  surrounded  by  mountains, 
some  of  which  rise  to  a  height  of  from  two  to  three  thousand  feet  above  the 
level  of  the  lake,  will  have  such  an  influence  upon  the  atmosphere  as  to 
vitiate  to  some  extent  the  accuracy  of  barometric  calculations.  No  numer- 
ical value  can  be  assigned  to  this  disturbing  factor.  In  some  of  the  remain- 
ing cases  there  were  special  peculiarities,  which  possibly  had  some  influence 
upon  the  computed  results,  and  there  are  only  six  or  eight  cases  left  which 
baffle  all  attempts  at  explanation. 

Taking  the  one  hundred  and  ten  favorable  cases  by  themselves,  the  aver- 
age difference  of  the  uncorrected  results  is  55.0  feet,  and  that  of  the  corrected 
results  is  19.1  feet,  a  reduction  of  about  sixty-five  per  cent.  The  average 
difference  of  the  uncorrected  results  in  the  thirty-six  unfavorable  cases  is 


96  BAROMETRIC   HYPSOMETRY. 

17.2  feet,  while  that  of  the  corrected  results  is  36.6  feet,  the  difference  being 
a  little  more  than  doubled.  Combining  the  favorable  and  the  unfavorable 
cases,  these  numbers  become,  Respectively,  45.7  and  23.5,  showing  that  on 
the  average  the  new  tables,  when  applied  to  observations  taken  in  Central  Cali- 
fornia, may  be  expected  to  reduce  such  discrepancies  by  about  one  half. 

There  now  remains  one  more  important  group  of  computations  to  be  ex- 
amined. At  a  great  many  points  visited  by  the  different  parties  in  the  field, 
a  series  of  barometric  observations  was  taken.  In  some  instances  the  series 
embraced  hourly  observations  for  several  days  in  succession,  and  in  others 
observations  were  taken  at  less  frequent  intervals,  though  extending  over 
several  days.  In  the  majority  of  cases  the  series  was  short,  comprising  only 
two  or  three  observations  taken  at  different  hours  of  the  same  day,  or  on 
different  days.  The  larger  part  of  these  observations  could  not  be  made 
directly  useful  in  the  subsequent  computations,  for  the  reason  that  there 
were  no  synchronous,  or  nearly  synchronous  observations  to  compare  with  at 
any  convenient  corresponding  station ;  but  in  all  cases  where  two  or  more 
observations  were  taken  at  any  field  station,  far  enough  apart  in  time  to  be 
regarded  as  independent  of  each  other,  for  which  suitable  corresponding 
observations  could  be  found,  as  many  independent  computations  as  possible 
were  made  to  determine  the  difference  of  altitude  between  the  field  station 
and  the  corresponding  station  selected  for  reference.  There  were  in  all  one 
hundred  and  seventy-one  such  cases.  In  one  case  as  many  as  forty-five 
independent  computations  were  made;  in  seventeen  cases  the  number  of 
computations  was  twenty  or  more;  and  there  were  fifty-seven  cases  for 
which  there  were  at  least  five  such  computations.  If  the  tables  in  ordinary 
use  always  gave  accurate  results,  the  several  calculated  differences  of  altitude 
for  any  given  pair  of  stations  ought  to  be  equal  to  each  other.  If  they  are 
not  equal,  there  is  a  source  of  error  somewhere,  which  requires  additional 
correction. 

That  there  is  a  real  advantage  to  be  gained  from  the  use  of  the  new  tables 
in  these  cases  may  be  made  to  appear  in  two  ways.  The  application  of  the 
corrections  ought  to  diminish  all  such  unconnected  differences  of  altitude  as 
are  already  too  high,  and  to  increase  such  as  are  too  low,  provided  there  is 
nothing  abnormal  in  any  of  the  observations  which  form  the  basis  of  the 
computation.  The  range  of  the  corrected  differences  of  the  altitude,  or  the 
absolute  difference  between  the  highest  and  the  lowest  of  the  several  deter- 


SUPPLEMENTARY  CHAPTER.  97 

minations,  therefore,  ought  to  be  less  than  that  of  the  uucorrected  differences. 
When  the  test  is  applied  in  this  form  to  the  one  hundred  and  seventy-one 
cases  now  under  consideration,  it  is  found  that  the  result  is  favorable  in  two 
thirds  of  the  instances,  and  unfavorable  in  the  remaining  one  third.  But 
this  method  of  testing  the  value  of  the  tables  is  imperfect.  It  not  unfre- 
q\iently  happens  that  just  those  values  of  the  uncorrected  differences  of 
altitude  which  are  farthest  from  the  mean  or  true  value  are  those  which  are 
abnormal  in  character ;  and  hence  the  application  of  the  corrections,  although 
it  may  bring  the  most  of  the  results  into  closer  harmony,  will  at  the  same 
time  cause  an  increase  in  the  range,  or  extreme  variation  from  the  mean 
value. 

The  other  method  of  estimating  the  worth  of  the  new  tables  is  more  satis- 
factory. An  examination  is  made  of  all  the  separate  results  in  detail,  for 
the  purpose  of  ascertaining  in  how  many  instances  the  application  of  the 
corrections  has  caused  the  uncorrected  difference  of  altitude  to  approach 
the  true  value  when  known,  or  the  mean  of  all  the  corrected  determinations 
(which,  in  the  absence  of  anything  more  definite,  will  have  to  be  accepted 
as  the  best  approximation  to  the  truth),  and  in  how  many  cases  the  reverse 
holds  true. 

The  table  on  the  following  pages  gives  the  details  of  a  number  of  cases  se- 
lected to  illustrate  these  two  methods.  The  columns  headed  I.  arid  II.  contain 
respectively  the  several  computed  differences  of  altitude  (with  their  range) 
between  the  field  stations  and  the  corresponding  stations  before  and  after 
the  application  of  the  corrections  from  the  new  tables.  Column  III.  contains 
the  variations  of  the  uncorrected  results  from  the  known  difference  of  alti- 
tude between  the  stations,  as  in  No.  3  (Blue  Canon  and  Summit)  and  in  No.  7 
(Gold  Eun  and  Colfax),  or  from  the  mean  of  the  corrected  results,  which  is 
assumed  to  be  a  close  approximation  to  the  truth,  when  the  true  difference 
is  not  known  from  other  sources.  Column  IV.  contains  similarly  the  varia- 
tions of  the  corrected  results.  The  numbers  in  column  IV.  will  be  smaller 
than  the  corresponding  numbers  in  column  III.,  whenever  the  application  of 
the  correction  has  diminished  the  error  of  the  uncorrected  result,  and  larger, 
whenever  the  error  has  been  increased. 


98 


BAROMETRIC  HYPSOMETRY. 


TABLE  SHOWING  THE  RANGE  AND  THE  ERRORS  OF  THE  UNCORRECTED 
AND  THE  CORRECTED  DIFFERENCES  OF  ALTITUDE  BETWEEN  TWO 
STATIONS. 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

I. 

H. 

in. 

IV. 

Uncor- 
rected. 

Range. 

Cor- 
rected. 

Range. 

Uncor- 
rected. 

Cor- 
rected. 

1 

Riley  Lane's. 

Sinartsville 

May  25       9  P.M. 
«    26      7  A.M. 

Mean 

628.0 
633.0 

5.0 

624.7 
625.2 

0.5 

3.0 

8.0 

0.3 

0.2 

630.5 

625.0 

5.5 

0.3 

2 

Tompkins's. 

Smartsville 

June  20     910  P.M. 

"      21      7     A.M. 

Mean 

3806.4 
3847.4 

41.0 

3817.4 
3835.4 

18.0 

20.0 
21.0 

9.0 
9.0 

3826.9 

3826.4 

20.5 

9.0 

3 

Blue  Ca!ion. 

Summit. 

Aug.  13    22S*p.M. 

2371.0 

2310.0 

34.9 

26.1 

Sept.  12     780A.M. 
«      12  12*°^. 

2296.0 
2389.2 

93.2 

2319.0 
2345.2 

35.2 

40.1 
53.1 

17.1 
9.1 

«     12    6"  P.M. 
Mean 

2312.0 

2312.0 

24.1 

24.1 

2342.0 

2321.5 

38.0 

19.1 

4 

Murphy's. 

Summit. 

Aug.  27    730  A.M. 

4805.5 

4841.5 

17.1 

18.9 

"    27    2    P.M. 
"    27    9    P.M. 

4952.5 
4740.2 

212.3 

4827.3 
4784.3 

57.2 

129.9 
82.4 

4.7 
38.3 

«    29    7    A.M. 
Mean 

4792.6 

4837.2 

30.0 

14.6 

4822.7 

4822.6 

64.8 

19.1 

5 

Columbia. 

Summit. 

Aug.  30      7  A.M. 

4833.9 

4878.8 

26.0 

18.9 

. 

"     30     2  P.M. 
"    30      9  P.M. 

5001.9 
4785.6 

216.3 

4875.9 
4830.1 

48.7 

142.0 
74.3 

16.0 
29.8 

"      31        7  A.M. 

Mean 

4810.0 

4854.8 

49.9 

5.1 

4857.8 

4859.9 

73.0 

17.4 

6 

Dutch  Flat 

Colfax. 

Oct.   27     2  P.M. 

757.3 

746.3 

12.3 

1.3 

Hotel. 

«     27      9  P.M. 

734.8 

29.8 

745.9 

3.5 

10.2 

0.9 

«<    28     7  A.M. 
Mean 

727.5 

742.8 

17.5 

2.2 

739.9 

745.0 

13.3 

1.5 

SUPPLEMENTARY  CHAPTER. 


99 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

i. 

II. 

HI. 

IV. 

Uncor- 
rected 

Range 

Cor- 
rected. 

Range. 

Uncor- 
rected. 

Cor- 
rected. 

7 

Gold  Run. 

Colfax. 

Oct.     7      7  A.M. 

787.5 

804.2 

22.0 

5.3 

"72  P.M. 

829.5 

814.3 

.  20.0 

4.8 

"79  P.M. 

790.5 

802.5 

19.0 

7.0 

"87  A.M. 

"      9      2  P.M. 

795.6 
835.7 

812.6 

820.5 

13.9 
26.2 

3.1 
11.0 

"99  P.M. 

792.1 

804.3 

17.4 

5.2 

"10        7  A.M. 

790.9 

807.9 

18.6 

1.6 

"    10      2  P.M. 

829.1 

813.9 

19.6 

4.4 

"      11         7  A.M. 

795.3 

56.6 

812.3 

29.8 

14.2 

2.8 

"       11         S^P.M. 

829.7 

819.7 

20.2 

10.2 

"       11         9  P.M. 

780.9 

792.7 

28.6 

16.8 

"       12         7  A.M. 

799.1 

816.1 

10.4 

6.6 

"     12      2  P.M. 

827.9 

812.7 

18.4 

3.2 

"    12      9  P.M. 

789.4 

801.4 

20.1 

8.1 

"      13        7  A.M. 

779.1 

796.7 

30.4 

12.8 

"     13      2  P.M. 

824.7 

809.6 

15.2 

0.1 

"13      9  P.M. 
Mean 

791.9 

803.9 

17.6 

5.6 

804.1 

808.5 

19.5 

6.4 

8 

Nevada  City. 

Smartsville 

July  U    lO^A.M. 

1740.6 

1696.0 

22.2 

22.4 

«     14      2  P.M. 

1780.9 

1717.9 

62.5 

0.5 

"     14      7  P.M. 

1719.6 

1700.7 

1.2 

17.7 

"      15         7  A.M. 

1786.2 

1768.3 

67.8 

49.9 

"    15      2  P.M. 

1790.5 

1727.5 

72.1 

9.1 

"    15      7  P.M. 

1766.2 

1746.8 

47.8 

28.4 

"    16      2  P.M. 

1784.5 

1721.5 

66.1 

3.1 

"    16      7  P.M. 

1703.5 

99.1 

1684.8 

942 

14.9 

33.6 

"      17         7  A.M. 

1730.1 

1712.8 

11.7 

5.6 

"    18      2  P.M. 

1802.6 

1738.9 

84.2 

20.5 

"    18      7  P.M. 

1734.1 

1715.0 

15.7 

3.4 

"       19         7  A.M. 

1716.6 

1699.4 

1.8 

19.0 

"19      2  P.M. 

1735.4 

1674.1 

17.0 

44.3 

"    19      7  P.M. 

1765.8 

1746.4 

47.4 

28.0 

"    20      7  A.M. 
Mean 

1742.7 

1725.3 

24.3 

6.9 

1753.3 

1718.4 

37.1 

19.5 

9 

Nevada  City. 

Dutch  Flat 

July  27      7  A.M. 

690.8 

694.7 

16.1 

20.0 

"     28      2  P.M. 

682.7 

664.7 

8.0 

10.0 

100 


BAROMETRIC  HYPSOMETRY. 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

i. 

II. 

III. 

IV. 

Uncor- 
rected. 

lange. 

Cor- 
rected. 

lange. 

Uncor- 
rected. 

Cor- 
ected. 

9 

Nevada  City 
(Continued). 

Dutch  Flat 

July  29       7  A.M. 
«     29      2  P.M. 

700.7 

685.9 

704.6 
667.9 

26.0 
11.2 

29.9 

6.8 

•«     29      7  P.M. 

676.9 

675.2 

2.2 

0.5 

"     30      7  A.M. 

669.0 

672.7 

5.7 

2.0 

"30      2  P.M. 

682.1 

664.1 

7.4 

10.6 

"30      7  P.M. 

665.7 

667.4 

9.0 

7.3 

"31         7  A.M. 

667.0 

670.7 

7.7 

4.0 

«     31      2  P.M. 

671.3 

653.7 

3.4 

21.0 

Aug.     1        7  A.M. 

664.3 

668.0 

10.4 

6.7 

"12  P.M. 

690.4 

672.3 

15.7 

2.4 

"17  P.M. 

680.1 

681.8 

5.4 

7.1 

"27  A.M. 

"22  P.M. 

678.0 
682.5 

49.3 

681.7 
664.6 

58.2 

3.3 

7.8 

7.0 
10.1 

"27  P.M. 

667.9 

666.2 

6.8 

8.5 

"         3        730A.M. 

676.6 

680.3 

1.9 

5.6 

"32  P.M. 

694.5 

676.3 

19.8 

1.6 

"37  P.M. 

666.0 

664.3 

8.7 

10.4 

"47  A.M. 

664.7 

668.4 

10.0 

6.3 

"42  P.M. 

694.3 

678.1 

19.6 

3.4 

"47  P.M. 

672.6 

670.9 

2.1 

3.8 

"57  A.M. 

673.1 

676.8 

1.6 

2.1 

"52  P.M. 

678.6 

660.8 

3.9 

13.9 

"57  P.M. 

713.6 

711.9 

38.9 

37.2 

"68  A.M. 

666.3 

667.6 

8.4 

7.1 

"62  P.M. 

697.7 

679.4 

23.0 

4.7 

"67  P.M. 
Mean 

689.3 

687.6 

14.6 

12.9 

680.1 

674.7 

10.7 

9.4 

10 

You  Bet. 

Colfax. 

Nov.  10      9  P.M. 

576.4 

585.3 

19.0 

27.9 

"      11         7A.M. 

552.7 

564.5 

4.7 

7.1 

"       11          145P.M 

583.2 

572.5 

25.8 

15.1 

"      11         728P.M 

561.1 

568.3 

3.7 

10.9 

"12         7  A.M. 

585.4 

597.9 

28.0 

40.5 

"     16      2  P.M. 

568.5 

562.2 

11.1 

4.8 

"16      9  P.M. 

532.5 

540.6 

24.9 

16.8 

"      17        7A.M. 

539.5 

551.0 

17.9 

6.4 

"      17         1  P.M. 

558.7 

552.8 

1.3 

4.6 

"    18      2  P.M. 

557.1 

550.8 

0.3 

6.6 

"    19      2  P.M. 

565.7 

559.4 

7-3 

2.0 

SUPPLEMENTARY  CHAPTER. 


101 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

L 

H. 

III. 

IV. 

Uncor- 
rected 

Range. 

Cor- 
rected. 

Range 

Uncor- 
rected. 

Cor- 
rected. 

10 

You  Bet 
(Continued). 

Colfax. 

Nov.  20        730A.M. 

"     20      2  P.M. 

546.8 
550.7 

57.0 

557.6 

544.5 

58.0 

10.6 
6.7 

0.2 
12.9 

"     20      9  P.M. 

534.7 

542.8 

22.7 

14.6 

••    21      7  A.M. 

537.8 

549.3 

19.6 

8.1 

"     21      2  P.M. 

564.2 

557.9 

6.8 

0.5 

"    21      9  P.M. 

532.5 

540.6 

24.9 

16.8 

"    22      7  A.M. 

528.4 

539.9 

29.0 

17.5 

«     23      7  A.M. 

538.4 

549.9 

19.0 

7.5 

Dec.      8        2  P.M. 

566.3 

563.2 

•  8.9 

5.8 

"89  P.M. 

556.8 

564.0 

0.8 

6.6 

"         9         7A.M. 

541.6 

553.1 

15.8 

4.3 

«       12         7  A.M. 

546.4 

557.9 

11.0 

0.5 

••     12      7  P.M. 
Mean 

544.8 

551.7 

12.6 

5.7 

552.9 

557.4 

13.8 

10.2 

11 

Lone  Pine. 

Smai-tsville 

May  17       7  A.M. 

3113.4 

3125.9 

68.7 

56.2 

"      17        3KA.TA. 

3184.8 

3174.0 

2.7 

8.1 

"       17         1   P.M. 

3278.7 

3223.0 

96.6 

40.9 

«•     17      6«p.M. 

3239.5 

3239.5 

57.4 

57.4 

"     17      9  P.M. 

3159.1 

3178.1 

23.0 

4.0 

"      18        7  A.M. 

3102.7 

3115.2 

79.4 

66.9 

«     18    12«°p.M. 

3240.9 

3191.6 

58.8 

9.5 

"     18      9  P.M. 

3186.5 

3205.6 

4.4 

23.5 

"     19      7  A.M. 

3169.1 

3181.7 

13.0 

0.4 

"      19        9  A.M. 

3208.8 

3203.0 

26.7 

20.9 

»     19    12  M. 

3267.5 

3224.2 

85.4 

42.1 

»     19      23°p.M. 

3255.1 

3195.3 

73.0 

13.2 

"     19      9  P.M. 

3232.5 

3251.9 

50.4 

69.8 

"    20      730A.M. 

3261.0 

3270.1 

78.9 

88.0 

«    20      S^P.M. 

3283.1 

3229.7 

101.0 

47.6 

"    20      9  P.M. 

3177.3 

3196.4 

4.8 

14.3 

"      21         7  A.M. 

3156.2 

3143.5 

25.9 

38.6 

"      21         9  A.M. 

3203.7 

3197.9 

21.6 

15.8 

"    21     12  M. 
"     21      2  P.M. 

3270.9 
3279.2 

219.7 

3227.6 
3218.3 

194.4 

88.8 
97.1 

45.5 
36.2 

"    21      4  P.M. 

3280.1 

3233.3 

98.0 

51.2 

«     21       9  P.M. 

3125.6 

3144.3 

56.5 

37.8 

«     22      7  P.M. 

3160.4 

3164.2 

21.7 

17.9 

"     22      9  P.M. 

3130.2 

3148.9 

51.9 

33.2 

BAROMETRIC   HYPSOMETRY. 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

I. 

II. 

III. 

IV. 

Uncor- 
rected. 

Range. 

Cor- 
rected. 

lange. 

Uncor- 
rected. 

Cor- 
rected. 

11 

Lone  Pine. 
(Continued). 

Smarts  ville 

May  23        7  A.M. 

«    23      9  P.M. 

3074.2 
3135.4 

3086.5 
3154.1 

107.9 
46.7 

95.6 

28.0 

«     24      7  A.M. 

3063.4 

3075.7 

118.7 

106.4 

"    24    12  M. 

3225.2 

3181.9 

43.1 

0.2 

••     24      2  P.M. 

3233.1 

3173.0 

51.0 

9.1 

"     24      4  P.M. 

3232.9 

3176.7 

50.8 

5.4 

"     24      9  P.M. 

3141.4 

3160.3 

40.7 

21.8 

«    25      7  A.M. 

3103.4 

3115.8 

78.7 

66.3 

•«    25      9  A.M. 

3160.6 

3154.9 

21.5 

27.2 

•<    25    12  M. 

3245.3 

3202.0 

63.2 

19.9 

"    25      2  P.M. 

3232.6 

3172.5 

50.5 

9.6 

"    25      9  P.M. 

3135.6 

3154.4 

46.5 

27.7 

"    26      7  A.M. 

3175.1 

3187.8 

7.0 

5.7 

«    26      g^A-M. 
Mean 

3251.7 

3242.6 

69.6 

60.5 

3194.1 

3182.1 

54.8 

34.8 

12 

Bend  City. 

Smartsville 

May  28        7°-5A.M. 

3088.2 

3092.8 

6.1 

10.7 

"     28      9  A.M. 

3184.8 

3172.1 

102.7 

90.0 

»    28      2  P.M. 

3307.7 

3227.5 

225.6 

145.4 

«    28      4  P.M. 

3324.3 

3256.4 

242.2 

174.3 

»    28      9  P.M. 

3200.6 

3215.6 

118.5 

133.5 

"    29      780A.M. 

3296.4 

3301-3 

214.3 

219.2 

«<    30    12  M. 

3178.5 

3120.7 

96.4 

38.6 

«    30      2  P.M. 

3162.0 

3085.2 

79.9 

3.1 

"    30      4  P.M. 

3191.3 

3126.1 

109.2 

44.0 

"    30      9  P.M. 

3121.3 

3106.6 

39.2 

24.5 

«      31         7  A.M. 

3051.9 

3061.7 

30.2 

20.4 

«      31         S^A.M. 

3097.6 

3091.1 

15.5 

9.0 

"    31      2  P.M. 

3216.5 

3138.7 

134.4 

56.6 

"    31      7  P.M. 

3043.7 

3034.3 

38.4 

47.8 

June     1        7  A.M. 

3032.9 

3042.6 

49.2 

39.5 

"          1         816A.M 

3075.5 

3069.0 

6.6 

13.1 

"          1       11   A.M. 

3111.8 

3072.0 

29.7 

10.1 

"          1       12  M. 

3125.5 

3008.6 

43.4 

13.5 

"12  P.M. 
"14  P.M. 

3154.5 
3149.2 

388.3 

3077.9 
3084.9 

355.9 

72.4 
67.1 

4.2 
2.8 

"19  P.M. 

3075.0 

3089.4 

7.1 

7.3 

"27  A.M. 

3034.5 

3044.2 

47.6 

37.9 

"29  A.M. 

3165.7 

3153.0 

83.6 

70.9 

SUPPLEMENTARY   CHAPTER. 


103 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

L 

II. 

III. 

IV. 

Uncor- 
rected 

Range. 

Cor- 
rected, 

Range. 

Uncor- 
rected. 

Cor- 
rected. 

12 

Bend  City 
(Continued). 

Smartsville 

June     2       2  P.M. 
"24  P.M. 

3148.9 
3034.2 

3072.3 
2972.4 

66.8 
47.9 

9.8 
109.7 

"28  P.M. 

2994.8 

2999.9 

97.3 

82.2 

"         3         7  A.M. 

2963.0 

2972.5 

119.1 

109.6 

"         3      1080A.M." 

3063.4 

3025.2 

18.7 

56.9 

«      3    12»p.M. 

3095.5 

3031.7 

13.4 

50.4 

"      3      48°p.M. 

3117.4 

3063.0 

35.3 

19.1 

«         4         710A.M. 

2979.0 

2988.5 

103.1 

93.6 

"47  P.M. 

3128.0 

3118.3 

45.9 

36.2 

"57  A.M. 

2936.0 

2945.4 

146.1 

136.7 

"      5      315P.M. 

3166.0 

3089.4 

83.9 

7.3 

"67  A.M. 

2984.1 

2993.7 

98.0 

88.4 

"       6      S^P.M. 

3138.7 

3069.7 

56.6 

12.4 

"69  P.M. 

3032.2 

3046.5 

49.9 

35.6 

"77  A.M. 

Mean 

2988.8 

2998.4 

93.3 

83.7 

3109.5 

3082.1 

77.2 

56.5 

13 

Camp  37. 

Smarts  ville 

June  27       4  P.M. 

5148.7 

5031.4 

281.5 

164.2 

"27      9  P.M. 

4929.1 

4951.3 

61.9 

84.1 

"    28      7  A.M. 

4981.3 

5000.7 

114.1 

133.5 

"    28      9  A.M. 

5103.0 

5083.1 

235.8 

215.9 

"    28    12  M. 

5211.3 

5107.1 

344.1 

239.9 

"    28      2  P.M. 

5230.4 

5090.7 

363.2 

223.5 

"    28      9  P.M. 

4943.6 

4965.8 

76.4 

98.6 

"    29      7  A.M. 

4884.7 

4903.7 

17.5 

36.5 

"    29      9  A.M. 

4954.1 

4934.8 

86.9 

67.6 

"    29    12  M. 

5055.9 

4954.7 

188.7 

87.5 

"    29      2  P.M. 

5084.6 

4950.8 

217.4 

83.6 

"    29      9  P.M. 

4899.6 

4921.7 

32.4 

54.5 

"    30      7  A.M. 

4805.5 

4824.2 

61.7 

43.0 

"    30      g^M. 

4912.6 

4878.2 

45.4 

11.0 

"    30    12  M. 

4957.2 

4858.1 

90.0 

9.1 

"    30      2  P.M. 

4999.9 

4866.4 

132.7 

0.8 

"    30      4  P.M. 

4998.4 

4884.9 

131.2 

17.7 

"     30      9  P.M. 

4832.3 

4854.4 

34.9 

12.8 

July     1       7  A.M. 

"19  A.M. 

4724.6 
4780.5 

527.0 

4743.0 
4761.9 

385.4 

142.6 

86.7 

124.2 
105.3 

"         1      1215P.M. 

4892.9 

4782.1 

25.7 

85.1 

"12  P.M. 

4948.5 

4816.3 

81.3 

50.9 

"14  P.M. 

4976.4 

4862.9 

109.2 

4.3 

104 


BAROMETRIC   HYPSOMETRY. 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

I. 

II. 

III. 

IV. 

Uncor- 
rected 

Range. 

Cor- 
rected. 

Range. 

TJncor- 
rected. 

Cor- 
rected. 

13 

Camp  37 
(Continued). 

Smartsville 

July      1        9  P.M. 
"27  A.M. 

4836.4 
4716.4 

4858.5 
4734.8 

30.8 
150.8 

8.7 
132.4 

"29  A.M. 

4804.7 

4786.0 

62.5 

81.2 

2     12  M. 

4874.0 

4776.5 

6.8 

90.7 

"22  P.M. 

4902.2 

4771.4 

35.0 

95.8 

"24  P.M. 

4910.3 

4799.1 

43.1 

68.1 

"29  P.M. 

4751.6 

4772.9 

115.6 

94.3 

"37  A.M. 

4703.4 

4721.7 

163.8 

145.5 

"         3         930A.M. 

4836.1 

4806.1 

31.1 

61.1 

"      3      285p.M. 

4925.6 

4793.6 

58.4 

73.6 

"39  P.M. 

4802.8 

4824.8 

64.4 

42.4 

"47  A.M. 

4722.3 

4740.7 

144.9 

126.5 

"         4         l^P.M. 

4963.6 

4834.9 

96.4 

32.3 

"58  A.M. 

4870.4 

4870.4 

3.2 

3.2 

"         5         l^P.M. 

5005.4 

4875.4 

138.2 

8.2 

"59  P.M. 

Mean 

4804.0 

4826.0 

63.2 

41.2 

4915.0 

4867.2 

106.9 

78.4 

14 

Gregory  Flat. 

Smartsville 

July  14      2  P.M. 

6728.6 

6550.4 

200.1 

21.9 

"      15         7  A.M. 

6445.9 

6476.9 

82.6 

51.6 

"     15      23°p.M. 

6764.7 

6586.1 

236.2 

57.6 

"     15      9  P.M. 

6465.7 

6496.8 

62.8 

31.7 

"       16         7  A.M. 

6491.0 

6522.2 

37.5 

6.3 

"     16      2  P.M. 

6751.6 

6572.7 

223.1 

48.2 

"     16      9  P.M. 

6456.3 

6487.4 

72.2 

41.1 

"      17         7  A.M. 

6465.5 

6496.6 

63.0 

31.9 

"      18        715A.M. 

6487.0 

6511.6 

41.5 

16.9 

"   18    ga'A.M. 

"    18      2  P.M. 

6585.4 
6785.0 

372.6 

6552.5 
6605.5 

172.8 

56.9 
256.5 

24.0 
77.0 

"    18      425P.M. 

6740.9 

6616.0 

212.4 

87.5 

"18      9  P.M. 

6412.4 

6443.2 

116.1 

85.3 

"       19         T^A-M. 

6488.1 

6507.6 

40.4 

20.9 

"       19         9  A.M. 

6551.1 

6532.8 

22.6 

4.3 

«       19      11   A.M. 

6656.1 

6572.3 

127.6 

43.8 

"    19      2  P.M. 

6752.3 

6573.4 

223.8 

44.9 

"     19      4  P.M. 

6647.2 

6500.9 

118.7 

27.6 

"     19      9  P.M. 

6417.8 

6448.6 

110.7 

79.9 

"    20      7  A.M. 
Mean 

6485.3 

6516.5 

43.2 

12.0 

6578.9 

6528.5 

117.4 

40.7 

SUPPLEMENTARY  CHAPTER. 


105 


Field  Station. 

orrespond- 
ing 
Station. 

Date. 

L 

H. 

III. 

IV. 

[Jncor- 
rected. 

Range. 

Cor- 
rected. 

flange. 

'ncor- 
ected. 

Cor- 
ected. 

15 

Gregory  Flat. 

Nevada 
City. 

uly  14    lO^A.M. 

«      14        2  P.M. 

4928.8 
4934.9 

879.5 
4804.0 

40.0 

46.1 

90.7 
15.2 

"      15        7  A.M. 

4729.8 

4752.6 

59.0 

36.2 

«     15      2  P.M. 

4933.4 

4802.5 

144.6 

13.7 

"     15      7  P.M. 

4828.0 

4813.5 

39.2 

24.7 

«      16         7  A.M. 

4693.8 

4716.3 

95.0 

72.5 

«16      2  P.M. 

4914.9 

4784.5 

126.1 

4.3 

«     16      7  P.M. 

4865.2 

4850.6 

76.4 

61.8 

"17        7  A.M. 

4765.9 

4788.7 

22.9 

0.1 

"     17      2  P.M. 

4976.0 

4844.0 

187.2 

55.2 

"    17      7  P.M. 

4822.9 

4808.4 

34.1 

19.6 

"       18         716A.M. 

4797.9 

4816.1 

9.1 

27.3 

«     18      2  P.M. 

4911.6 

4781.5 

122.8 

7.3 

•«     18      7  P.M. 

4836.5 

4822.0 

47.7 

33.2 

"       19         710A.M. 

4738.0 

4756.2 

50.8 

32.6 

«     19      2  P.M. 

4941.6 

344.9 

4810.6 

226.2 

152.8 

21.8 

«     19      7  P.M. 

4808.5 

4794.1 

19.7 

5.3 

«    20      7  A.M. 

4770.4 

4793.2 

18.4 

4.4 

"      20      10  A.M. 

4818:9 

4783.9 

30.1 

4.9 

"20      2  P.M. 

4862.1 

4733.3 

73.3 

55.5 

"    20      4  P.M. 

4951.5 

4842.6 

162.7 

53.8 

"    20      7  P.M. 

4816.1 

4801.7 

27.3 

12.9 

«    21      7  A.M. 

4631.1 

4653.3 

157.7 

135.5 

"      21       11   A.M. 

4829.1 

4768.3 

40.3 

20.5 

"    21      2  P.M. 

4939.5 

4808.5 

150.7 

19.7 

"     21      4  P.M. 

4927.3 

4819.0 

138.5 

30.2 

«    21      7  P.M. 

4818.5 

4804.0 

29.7 

15,2 

«    22      7  A.M. 

4791.0 

4818.0 

2.2 

29.2 

"     22      2  P.M. 

4841.8 

4713.5 

53.0 

75.3 

"     22      7  P.M. 

4770.6 

4756.3 

18.2 

32.5 

"     23      7  A.M. 
Meai 

4711.6 

4734.1 

77.2 

54.7 

4835.7 

4788.8 

79.1 

34.4 

16 

Camp  9. 

Colfax. 

Sept.  21        9  P.M. 

1353.2 

1369.6 

22.1 

5.7 

• 

"     22      7  A.M. 

1346.8 

1361.4 

28.5 

13.9 

"    22      2  P.M. 

1405." 

1371.8 

30.4 

3.5 

"     22      9  P.M. 

1322.0 

1338.6 

52.8 

36.7 

"     23      7  A.M. 

1397.6 

1412.7 

22.3 

37.4 

"     23      2  P.M. 

1431.8 

1397.2 

56.6 

21.9 

106 


BAROMETRIC   HYPSOMETRY. 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

L 

II. 

III. 

IV. 

Uncor- 
rected 

Range. 

Cor- 
rected. 

Range. 

TJncor- 
rected. 

Cor- 
rected. 

16 

Camp  9 
(Continued). 

Colfax. 

Sept.  23        9  P.M. 

«     24      7  A.M. 
"    24      2  P.M. 

1365.5 
1369.8 
1397.5 

109.4 

1381.9 
1384.6 
1363.6 

74.1 

9.8 
5.5 
22.2 

6.6 
9.3 
11.7 

"     24      9  P.M. 

1365.9 

1382.3 

9.4 

7.0 

"     25      7  A.M. 

1366.8 

1381.6 

8.5 

6.3 

«    25      2  P.M. 

1389.9 

1356.1 

14.6 

19.2 

"     25      9  P.M. 

1353.9 

1370.3 

21.4 

5.0 

«     26      7  A.M. 

1355.6 

1370.2 

19.7 

5.1 

«    26      2  P.M. 

1389.2 

1355.4 

13.9 

19.9 

«     26      9  P.M. 
Mean 

1390.8 

1407.7 

15.5 

32.4 

1375.2 

1375.3 

22.1 

15.1 

17 

Lakeport. 

Sacramento 

Oct.    19      7  A.M. 

1247.3 

1269.7 

76.5 

54.1 

«     19      2  P.M. 

1353.5 

1323.2 

29.7 

0.6 

«     19      9  P.M. 

1231.2 

1250.7 

92.6 

73.1 

«    20      7  A.M. 

1237.5 

1259.7 

86.3 

64.1 

»    20      2  P.M. 

1369.9 

1339.1 

46.1 

15.3 

«     20      9  P.M. 

1249.3 

1269.1 

74.5 

54.7 

»    21       7  A.M. 

1259.8 

1282.4 

64.0 

41.4 

«    21      2  P.M. 

1386.9 

1355.7 

63.1 

31.9 

»     21      9  P.M. 

1321.3 

1342.1 

2.5 

18.3 

"     22      7  A.M. 

1316.1 

1339.7 

7.7 

15.9 

«     22      2  P.M. 

1386.3 

1355.1 

62.5 

31.3 

«    23      7  A.M. 

1333.1 

1357.0 

9.3 

33.2 

«    23      2  P.M. 
<«     23      9  P.M. 

1332.7 
1287.0 

183.2 

1302.7 
1307.3 

131.9 

8.9 
36.8 

21.1 
16.5 

«    24      7A.M. 

1264.5 

1287.2 

59.3 

36.6 

«     24      2  P.M. 

1414.4 

1382.6 

90.6 

58.8 

"     24      9  P.M. 

1346.7 

1367.0 

22.9 

43.2 

«     25      7  A.M. 

1313.8 

1337.4 

10.0 

13.6 

«     25      2  P.M. 

1402.3 

1370.8 

78.5 

47.0 

«     25      9  P.M. 

1325.5 

1346.4 

1.7 

22.6 

«     26      7  A.M. 

1297.4 

1320.6 

26.4 

3.2 

<>    26      2  P.M. 

1354.9 

1324.5 

31.1 

0.7 

«    26      9  P.M. 

1336.6 

1357.7 

12.8 

33.9 

"     27      7  A.M. 

1282.5 

1305.4 

41.3 

18.4 

"     27      2  P.M. 

1407.2 

1375.6 

83.4 

51.8 

«     27      9  P.M. 
Mean 

1270.8 

1290.9 

53.0 

32.9 

1320.3 

1323.8 

45.1 

32.1 

SUPPLEMENTARY  CHAPTER. 


107 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

i. 

II. 

III. 

IV. 

Uncor- 
rected. 

Range. 

Cor- 
rected. 

lange. 

Uncor- 
rected. 

Cor- 
rected 

18  Damascus. 

Summit. 

June      1        9  P.M. 

2971.9 

2984.7 

57.2 

44.4 

"29  P.M. 

3013.1 

3026.0 

16.0 

3.1 

"37  A.M. 

»39  P.M. 

3032.9 
3035.5 

178.5 

3042.0 
3048.5 

107.1 

3.8 
6.4 

12.9 
19.4 

"      4    12  M. 

3150.4 

3090.2 

121.3 

61.1 

"        5        718A.M. 

Mean 

2977.1 

2983.1 

52.0 

46.0 

3030.1 

3029.1 

42.8 

31.1 

19 

Michigan  Bluff 

Colfax. 

June  15      9  P.M. 

1053.4 

1057.9 

9.9 

5.4 

»     16      7  A.M. 

1071.9 

1075.1 

8.6 

11.8 

•<     16      2p.M. 

1085.4 

1056.2 

22.1 

7.1 

"     16      9  P.M. 

1071,3 

1075.9 

8.0 

12.6 

"17        7  A.M. 

1062.9 

1066.1 

0.4 

2.8 

"17      2  P.M. 

1085.0 

1055.8 

21.7 

7.5 

"    17      e^p.M. 

1053.6 

1045.9 

9.7 

17.4 

"    17      9  P.M. 

1062.6 

1067.0 

0.7 

3.7 

"      18        1»P.M. 

1069.6 

1041.6 

6.3 

21.7 

"     19    1245P.M. 

1095.4 

49.3 

1069.1 

46.1 

32.1 

5.8 

"     19      9  P.M. 

1059.1 

1063.6 

4.2 

0.3 

"     20      7  A.M. 

1084.4 

1087.7 

21.1 

24.4 

"    20      4I5P.M. 

1063.6 

1043.9 

0.3 

19.4 

"     20      9  P.M. 

1061.8 

1066.3 

1.5 

3.0 

"      21          7  A.M. 

1056.7 

1059.9 

6.6 

3.4 

"     21      2  P.M. 

1097.0 

1067.4 

33.7 

4.1 

"    21      9  P.M. 

1047.7 

1052.2 

15.6 

12.1 

"     22      845A.M. 

1080.4 

1076.1 

17.1 

12.8 

"    22      9  P.M. 
Mean 

1070.3 

1074.9 

7.0 

11.6 

1070.1 

1063.3 

11.9 

9.8 

20 

Forest  Hill. 

Colfax. 

June  26      7  A.M. 

809.0 

812.2 

0.4 

3.6 

"    26      215P.M 

823.9 

801.8 

15.3 

6.8 

"    26      9  P.M. 

777.7 

781.2 

30.9 

27.4 

"    27      T^A.M 

803.4 

805.5 

5.2 

3.1 

"     28      8  A.M. 

811.8 

811.8 

3.2 

3.2 

"    28    1015A.M 

814.3 

806.4 

5.7 

2.2 

"     28    ^P.M 

825.2 

806.6 

16.6 

2.0 

"     28      T^P.M 

811.8 

810.8 

3.2 

2.2 

"     28      9  P.M. 

801.5 

805.1 

7.1 

3.5 

108 


BAROMETRIC  HYPSOMETRY. 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

i. 

II. 

III. 

IV. 

Uncor- 
rected 

Range. 

Cor- 
rected. 

Range. 

Uncor- 
rected. 

Cor- 
rected. 

20 

Forest  Hill 
(Continued). 

Colfax. 

June  29       S^A.M. 
«      29     lO^A.M. 

811.3 
818.9 

809.7 
809.9 

2.7 
10.3 

1.1 
1.3 

«     29      6«p.M. 

823.1 

818.9 

14.5 

10.3 

"      30         S^A.M. 

802.5 

69.0 

801.0 

43.5 

6.1 

7.6 

"      30     10  A.M. 

816.1 

809.2 

7.5 

0.6 

"    30    12  M. 

826.4 

809.9 

17.8 

1.3 

July      1        S^A-M. 

816.7 

813.6 

8.1 

5.0 

<•         2        9WA.M. 

795.0 

791.0 

13.6 

17.6 

"38  A.M. 

807.1 

807.0 

1.5 

1.6 

"49  A.M. 

819.4 

816.2 

10.8 

7.6 

"         6        915A.M. 

828.5 

824.4 

19.9 

15.8 

"      6    12  M. 

839.3 

822.5 

30.7 

13.9 

"79  A.M. 

827.9 

824.7 

19.3 

16.1 

"87  A.M. 

803.8 

807.0 

4.8 

1.6 

"87  P.M. 

796.0 

793.1 

12.6 

15.5 

"      10        9MA.M. 

Mean 

820.1 

816.3 

11.5 

7.7 

813.2 

808.6 

11.2 

7.1 

21 

Blacksmith 
Flat. 

Georgetown 

Sept  15       4  P.M. 
"    15      6  P.M. 

1195.5 
1154.7 

1177.0 
1152.4 

37.0 

3.8 

18.5 
6.1 

"     15      9  P.M. 

1135.4 

60.1 

1149.2 

27.8 

23.1 

9.3 

"      16        880A.M. 

1156.3 

1163.8 

2.2 

5.3 

"     16      5  P.M. 
Mean 

1161.1 

1150.0 

2.6 

8.5 

1160.6 

1158.5 

17.7 

9.5 

22 

Placerville. 

Colfax. 

Oct.      4        9  A.M. 

545.3 

551.3 

14.3 

8.3 

"42  P.M. 

575.7 

565.2 

16.1 

5.6 

"57  A.M. 

559.6 

571.5 

0.0 

11.9 

"52  P.M. 

579.8 

569.3 

20.2 

9.7 

"69  A.M. 

585.4 

591.8 

25.8 

32.2 

"62  P.M. 

588.7 

578.2 

29.1 

18.6 

««     7    g^A-M. 

566.5 

570.9 

6.9 

11.3 

"71   P.M. 

571.3 

561.8 

11.7 

2.2 

"74  P.M. 

568.1 

562.8 

8.5 

3.2 

"82  P.M. 

556.6 

546.5 

3.0 

13.1 

«<         9         9»A.M. 

549.6 

553.6 

10.0 

6.0 

"92  P.M. 

575.2 

53.7 

564.7 

50.9 

15.6 

5.1 

"     10      2  P.M. 

556.7 

546.6 

2.9 

13.0 

SUPPLEMENTARY  CHAPTER. 


109 


Field  Station. 

Correspond- 
ing 
Station. 

Date. 

i. 

II. 

in. 

IV. 

Uncor- 
rected. 

Range. 

Cor- 
rected. 

Range. 

Uncor- 
rected. 

Cor- 
rected 

22 

Placerville 
(Continued.) 

Colfax. 

Oct.    11         9«°A.M. 
"      11         2P.M. 

548.7 
571.6 

552.7 

561.1 

10.9 
12.0 

6.9 
1.5 

"       13         9  A.M. 

538.4 

544.3 

21.2 

15.3 

«•    13      3  P.M, 

559.3 

550.9 

0.3 

8.7 

"     14      2  P.M. 

562.0 

551.8 

2.4 

7.8 

••    16      2  P.M. 

557.4 

546.3 

2.2 

13.3 

"17        9  A.M. 

535.0 

540.9 

24.6 

18.7 

«•    20      2  P.M. 

571.5 

561.0 

11.9 

1.4 

"    21      9  A.M. 

562.8 

568.8 

3.2 

9.2 

"21        1  P.M. 

Mean 

573.0 

563.5 

13.4 

3.9 

563.4 

559.6 

11.6 

9.9 

19 

Geyser  Springs 

Colfax. 

Sept.  15      9  P.M. 

981.0 

993.0 

19.3 

31.3 

"       16         7  A.M. 

975.1 

985.7 

13.4 

24.0 

"     16      2  P.M. 

«     17      7  A.M. 

947.4 
960.4 

46.2 

924.4 
970.7 

80.8 

14.3 
1.3 

37.3 
9.0 

»17      2  P.M. 

934.8 

912.2 

26.9 

49.5 

"    17      9  P.M. 
Mean 

972.3 

984.1 

10.6 

22.4 

961.8 

961.7 

14.3 

28.9 

24 

Long  Valley. 

Colfax. 

Nov.    8      7  A.M. 

1046.7 

1062.9 

21.7 

5.5 

»82  P.M. 

1050.6 

1034.0 

17.6 

34.4 

»92  P.M. 

1039.0 

1022.6 

29.4 

45.8 

»99  P.M. 

1092.8 

53.8 

1106.9 

84.3 

24.4 

38.5 

"       13         7  A.M. 

1075.4 

1091.9 

7.0 

23.5 

««13      2  P.M. 

1071.7 

1054.9 

3.3 

13.5 

«    - 

"13      9  P.M. 

1089.6 

1103.7 

21.2 

35.3 

1066.5 

1068.4 

17.8 

28.1 

The  cases  cited  as  illustrations  have  been  selected  mainly  from  those  where 
a  large  number  of  independent  computations  have  been  made,  for  it  is  from 
the  study  of  such  cases  in  particular  that  the  real  worth  of  the  new  tables 
can  be  determined  most  satisfactorily.  .They  have  also  been  chosen  with  the 
view  of  illustrating  the  use  of  the  tables  under  a  considerable  variety  of  con- 
ditions, some  acquaintance  with  which,  as  well  as  with  the  geographical  posi- 
tions or  other  peculiarities  of  the  stations,  will  be  necessary  for  the  complete 


HO  BAROMETRIC   HYPSOMETRY. 

understanding  of  the  significance  of  each  case,  and  for  estimating  its  relative 
importance  compared  with  the  others.  The  geographical  relations  of  Sacra- 
mento, Colfax,  and  Summit  have  been  described  in  a  previous  chapter  (pages 
29  and  30).  Of  the  other  points  used  as  corresponding  stations,  Nevada 
City  and  Georgetown  are  practically  the  equivalent  of  Colfax,  the  former 
being  about  twelve,  and  the  latter  about  fifteen  miles  distant,  with  a  d.ffer- 
ence  of  altitude  not  exceeding  250  feet ;  Smartsville  lies  in  the  foot-hills  of 
Yuba  county,  at  an  altitude  of  762  feet  above  the  sea,  and  about  twenty  miles 
to  the  northwest  of  the  line  joining  Sacramento  and  Colfax ;  Dutch  Flat  is  a 
station  on  the  Central  Pacific  Eailroad,  thirteen  miles  above  Colfax;  the 
barometer  hung  in  the  banking-office  of  Messrs.  W.  &  P.  Nicholls,  at  a  point 
723  feet  above  the  barometer  at  Colfax. 

The  positions  of  the  field-stations  and  their  distances,  in  direct  lines,  from 
the  corresponding  stations  are  approximately  as  follows :  — 

1.  Riley  Lane's  is  in  the  valley  of  the  Sacramento  river,  a  few  miles  below 
Smartsville. 

2.  Tompkins's  is  at  the  head-waters  of  the  Yuba  river,  thirty-four  miles  from 
Smartsville. 

3.  Blue  Canon  is  a  station  on  the  Central  Pacific  Eailroad,  about  twenty  miles 
from  Summit. 

4  and  5.  Murphy's  and  Columbia  are  about  eighty-five  miles  nearly  due  south 
from  Summit,  and  do  not  differ  more  than  300  feet  in  altitude  from  Colfax. 

6,  8,  and  9.  The  positions  of  Dutch  Flat  and  Nevada  City  are  described  above. 

7.  Gold  Run  is  a  station  on   the  Central   Pacific   Railroad  ten  miles  above 
Colfax. 

10.  You  Bet  is  in  Nevada  county,  eight  miles  from  Colfax. 

11  and  12.  Lone  Pine  and  Bend  City  are  in  Owen's  Valley,  on  the  east  side 
of  the  Sierra  Nevada  mountains,  and  nearly  two  hundred  and  fifty  miles  from 
Smartsville. 

13,  14,  and  15.  Camp  37  and  Gregory  Flat  are  both  on  the  eastern  slope  of  the 
Sierra  Nevada  mountains ;  the  former  is  about  one  hundred  and  eighty  miles, 
the  latter  one  hundred  and  fifty,  southeast  of  Smartsville. 

16.  Camp  9  is  about  ten  miles  south  of  Clear  Lake,  and  ninety  miles  from 
Colfax. 

17.  Lakeport  lies  on  Clear  Lake,  eighty  miles  from  Sacramento. 

18.  Damascus  is  in  Placer  county,  about  thirty  miles  from  Summit. 


SUPPLEMENTARY   CHAPTER.  HI 

19  and  20.  Michigan  Bluff  and  Forest  Hill  are  in  Placer  county,  not  more  than 
twelve  miles  from  Colfax. 

21.  Blacksmith  Flat  is  in  El  Dorado  county,  a  few  miles  only  from  Georgetown. 

22.  Placerville  is  in  El  Dorado  county,  about  twenty-seven  miles  southerly  from 
Colfax. 

23  and  24.  Geyser  Springs  and  Long  Valley  are  both  in  the  region  visited  by 
the  Clear  Lake  party. 

An  inspection  of  the  preceding  table  will  show  that  in  all  but  the  last  two 
cases  the  average  errors  of  the  corrected  results  (the  means  in  column  IV.) 
are  less  than  those  of  the  uncorrected  results  (column  III.) ;  and  that  in  only 
a  little  more  than  one  quarter  of  the  individual  computations  (115  out  of 
402,  or  twenty-eight  per  cent)  has  the  error  of  the  uncorrected  results  been 
increased  by  the  application  of  the  correction.  Among  the  whole  number  of 
cases  from  which  those  in  the  tables  have  been  selected,  one  hundred  and 
seventy-one  in  all,  there  are  only  thirty  in  which  the  application  of  the  cor- 
rections has  increased  the  average  error,  and  of  these  only  five  can  properly 
be  called  bad  cases.  Two  of  these  five  are  given  in  the  table  (Nos.  23 
and  24).  Taking  all  the  one  hundred  and  seventy-one  cases  together,  involv- 
ing as  they  do  eleven  hundred  and  ninety-nine  separate  computations,  there 
are  three  hundred  and  seventy-eight  (or  thirty-one  and  six  tenths  per  cent) 
instances  where  the  use  of  the  new  tables  has  resulted  in  an  increase  of  the 
error,  although  in  the  most  of  the  instances  the  increase  has  been  slight. 
This  is  a  large  percentage,  it  is  true,  but  perhaps  no  larger  than  might  be 
expected,  when  all  the  adverse  conditions  are  taken  into  consideration. 

If  it  be  objected  that  there  is  no  sufficient  justification  for  taking  the 
means  of  the  corrected  results  (column  II.)  as  the  closest  attainable  approxi- 
mations to  the  real  differences  of  altitude  between  the  stations,  and  that  by 
so  doing  the  errors  of  the  corrected  results  (column  TV.)  may  have  been  made 
to  appear  less  than  they  otherwise  would,  the  reply  is,  that,  even  if  the 
means  of  the  uncorrected  results  (column  T.)  had  been  assumed  to  be  the 
true  differences  of  altitude,  it  would  not  have  affected  to  any  material  extent 
the  conclusions  to  be  drawn  from  the  study  of  columns  III.  and  IV.  as  they 
now  stand.  In  all  the  cases  cited  in  the  table,  excepting  Nos.  3,  8,  13,  14, 
and  15,  there  is  a  remarkably  close  agreement  between  the  mean  values  of 
the  uncorrected  and  the  corrected  results.  This  shows  that  the  mean  result 


112  BAROMETRIC   HYPSOMETRY. 

obtained  from  a  considerable  series  of  barometric  observations,  especially 
when  the  observations  are  taken  at  different  hours  of  the  day  and  extend 
over  several  days,  may  not  be  far  from  the  truth,  notwithstanding  the  wide 
variations  of  the  separate  computations  from  the  mean  value,  but  does  not 
establish  any  further  presumption  in  favor  of  its  accuracy.*  The  preponder- 
ance of  evidence,  derived  from  all  sources,  is  decidedly  in  favor  of  the  mean 
of  the  corrected  results. 

The  question  now  arises,  what  conclusion  can  be  drawn  from  the  results 
in  these  one  hundred  and  seventy-one  cases  as  to  the  advantage  gained  by 
using  the  new  tables  ?  The  most  satisfactory  way  of  meeting  this  question 
seems  to  be  to  ascertain  the  average  error  for  a  thousand  feet  of  difference 
of  altitude,  before  and  after  the  application  of  the  corrections.  The  aggregate 
of  all  the  differences  of  level  in  the  twenty-four  cases  cited  in  the  table  is 
54,772  feet.  The  aggregates  of  the  average  errors  in  columns  III.  and  IV. 
are  929.8  and  527.7  feet.  This  makes  the  average  errors  per  thousand  feet 
16.97  and  9.63  feet  respectively.  The  aggregate  of  the  differences  of  level 
in  the  one  hundred  and  seventy-one  cases  taken  together  is  279,592.6  feet, 
and  of  the  average  errors,  4,838.0  and  2,742.1  feet.  This  makes  the  average 
errors  per  thousand  feet  17.30  and  9.81  feet. 

The  conclusion,  therefore,  is  that,  roughly  speaking,  the  residual  errors  of 
the  computations  based  upon  the  old  tables  alone  are  reduced  about  one  half  by 
the  use  of  the  new  tables,  — a  conclusion  identical  with  that  reached  on  page  96, 
as  the  result  of  the  examination  of  one  hundred  and  forty-six  different  cases. 

*  According  to  the  tables  given  on  pages  87  and  88,  the  mean  of  the  day  is,  for  certain  months 
in  the  year,  almost  exactly  the  same  as  the  mean  of  the  year.  For  instance,  in  table  XXIV.,  the 
correction  to  be  applied  for  each  thousand  feet  from  sea-level  to  seven  thousand  feet  is,  in  June, 
-  1.9  ;  in  July,  + 1.0  ;  in  August,  +  2.6. 


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